# Publications

### From NA-Wiki

## Contents |

## Journal Articles

### 2008

- F. Nobile, R. Tempone and C. G. Webster, An anisotropic sparse grid stochastic collocation method for elliptic partial differential equations with random input data.
*Accepted for publication in SINUM, February 13, 2008*

- F. Nobile, R. Tempone and C. G. Webster, A sparse grid stochastic collocation method for elliptic partial differential equations with random input data.
*Accepted for publication in SINUM, February 5, 2008*

- E. Mordecki , A. Szepessy, R. Tempone and G. E. Zouraris, Adaptive weak approximation of diffusions with jumps.
*Accepted for publication in SINUM, January 2008*.

- J. Hoffman and C. Johnson, Blow up of incompressible Euler equations,
*BIT Numerical Mathematics*, to appear 2008.

- J. Hoffman and C. Johnson, Computational Foundation of Thermodynamics,
*Comput. Meth. Appl. Mech. Engrg.*, to appear 2008.

- J. Hoffman and C. Johnson, Resolution of d'Alemberts Paradox,
*J. Math. Fluid Mech.*, to appear 2008.

- J. Hoffman, Efficient computation of mean drag for the subcritical flow past a circular cylinder using General Galerkin G2,
*International Journal of Numerical Methods in Fluids*, to appear 2008.

- J. Jansson, A. Logg, Algorithms and Data Structures for Multi-Adaptive Time-Stepping,
*ACM Transactions on Mathematical Software*, accepted 2008.

### 2007

- O. Runborg. Mathematical models and numerical methods for high frequency waves.
*Commun. Comput. Phys.*, 2:827-880, 2007.

- I. Daubechies, O. Runborg and J. Zou. A sparse spectral method for homogenization multiscale problems.
*Multiscale Model. Sim.*, 6(3):711-740, 2007.

- M. Motamed and O. Runborg. A multiple-patch phase space method for computing trajectories on manifolds with applications to wave propagation problems.
*Commun. Math. Sci.*, 5(3):617--648, 2007.

- M. Hanke, K.H.A. Olsson and M. Strömgren. "Stability Analysis of a Degenerate Hyperbolic System Modelling a Heat Exchanger."
*Mathematics and Computers in Simulation*, 74(2007)1, 8-19

- T. Ali, M. Hanke and A. Loubenets. "Highly accurate finite element method for one-dimensional elliptic interface problems."
*Appl. Numer. Math.*, Accepted for publication

- B. Sjögreen, K. Gustavsson and R.L. Gudmundsson, A model for peak formation in the two-phase equations.
*Mathematics of Computation*,76:1925-1940, 2007.

- W. E, B. Engquist, X. Li, W. Ren and E. Vanden-Eijnden. Heterogeneous multiscale methods.
*Commun. Comput. Phys.*, 2, 367-450, 2007

- A. Atle and B. Engquist. On surface radiation conditions for high-frequency wave scattering.
*J. Comp. Appl. Math.*, 204, 306-316, 2007

- B. Engquist and L. Ying. Fast directional multilevel computation for problems with oscillatory kernels.
*SIAM J. Scientific Comp.*, 27, 1710-1737, 2007

- A. Abdulle and B. Engquist. Finite element heterogeneous multiscale methods with near optimal computational complexity.
*MMS*, 6, 1059-1084, 2007

- E. Olsson, G. Kreiss. and S. Zahedi. A conservative level set method for two phase flow II.
*for J Comput Phys*, vol 225, p785-807, 2007.

- I. Babuska and R. Tempone, "Static Frame Challenge Problem: Summary".
*Accepted for publication in CMAME, September 2007.*

- I. Babuska, F. Nobile and R. Tempone, "A systematic approach to model validation based on Bayesian updates and prediction related rejection criteria".
*Accepted for publication in CMAME, August 2007.*

- I. Babuska, F. Nobile and R. Tempone, "Formulation of the Static Frame Problem".
*Accepted for publication in CMAME, February 2007*

- I. Babuska, F. Nobile and R. Tempone, "A Stochastic Collocation method for elliptic Partial Differential Equations with Random Input Data".
*SIAM Journal of Numerical Analysis Vol. 45, No. 3, pp.1005-1034 (May 2007)*

- I. Babuska, F. Nobile and R. Tempone, "Reliability of Computational Science".
*Numerical Methods for Partial Differential Equations Vol. 23, No. 4, pp. 753-784 (July 2007)*

### 2006

- A.Jaun, A.Kaufman, E.R.Tracy,
*Eikonal waves, caustics and mode conversion in tokamak plasmas*, article, submitted, Plasma Phys. Contr. Fusion (2006)

- M. Motamed and O. Runborg. "A fast phase space method for computing creeping rays."
*J. Comput. Phys.*, 219:276-295, 2006.

- A.-K. Tornberg and K. Gustavsson. A Numerical Method for Simulations of Rigid Fiber Suspensions.
*Journal of Computational Physics*, 215:172-196, 2006.

- Sun Y. and B. Engquist. heterogeneous multiscale methods for interface tracking of combustion fronts.
*SIAM J. Multiscale Model. Simul.*, 5, 532-563, 2006

- E. Chung and B. Engquist. Optimal Discontinuous Galerkin Methods for Wave Propagation.
*SIAM J. Numer. Anal.,*44, 2131-2158, 2006

- A.-K. Tornberg, B. Engquist, B. Gustafsson and P, Wahlund. A new type of boundary treatment for wave propagation.
*BIT*, 46, S1, 145-170, 2006

- A.-K. Tornberg and B. Engquist. High order difference methods for wave propagation in discontinuous media.
*Meth. Appl. Analysis*, 13, 217-273, 2006

- D. Appelö and G. Kreiss. A new absorbing layer for elastic waves.
*J. Comp. Phy*, vol 215(2),p642-660, 2006.

- D. Appelö, T. Hagstrom and G. Kreiss. Perfectly matched layers for hyperbolic systems: General formulation, well-posedness and stability.
*SIAM J. App. Math.*, vol 67, no 1, p 1-23, 2006.

- P.-O. Åsen and G. Kreiss. Resolvent bounds for pipe Poiseuille flow.
*J Fluid Mech*, 568, pp. 451--471, 2006.

- A. Szepessy, M. Katsoulakis, Stochastic hydrodynamical limits of particle systems.
*Communications in Mathematical Sciences (CMS)*Vol 4, No. 3, September 2006.

- A. Szepessy, M. Sandberg, Convergence rates of Symplectic Pontryagin Approximations in Optimal Control Theory.
*M2AN Math. Model. Numer. Anal.*40 (2006), no. 1, 149--173.

- A. Szepessy, K.-S. Moon, E. von Schwerin and R. Tempone, Convergece rates of an adaptive dual weighted residual finite element algorithm.
*BIT Numerical Mathematics*(2006) 46, 367-407.

- J. Hoffman, Adaptive simulation of the sub-critical flow past a sphere,
*J. Fluid Mech., Vol.568, pp.77-88*, 2006.

- J. Hoffman and C. Johnson, A new approach to Computational Turbulence Modeling,
*Comput. Meth. Appl. Mech. Engrg., Vol.195, pp.2865-2880*, 2006.

- J. Hoffman and C. Johnson, Stability of the dual Navier-Stokes equations and efficient computation of mean output in turbulent flow using Adaptive DNS/LES,
*Comput. Meth. Appl. Mech. Engrg., Vol.195, pp.1709-1721*, 2006.

- J. Hoffman, Computation of turbulent flow past bluff bodies using adaptive General Galerkin methods: drag crisis and turbulent Euler solutions,
*Comp. Mech. Vol.38, pp.390-402*, 2006.

- J. Hoffman and C. Johnson, Irreversibility in Reversible Systems,
*HERMIS Int. J. Computer Mathematics and its Applications, Vol. 6*, 2006.

### 2005

- J. Möller, O. Runborg, P. G. Kevrekidis, K. Lust, and I. G. Kevrekidis. "Equation-free, effective computation for discrete systems: a time stepper based approach."
*Int. J. Bifurcat. Chaos*, 15:975-996, 2005.

- L. Gosse and O. Runborg. "Finite moment problems and applications to multiphase computations in geometric optics."
*Commun. Math. Sci.*, 3:373-392, 2005.

- L. Gosse and O. Runborg. "Resolution of the finite Markov moment problem."
*C. R. Math. Acad. Sci. Paris,*Ser I 341:775-780, 2005.

- M. Hanke, K.H.A. Olsson and M. Strömgren. " Stability Analysis of a a Reduced Heat Exchanger Model."
*PAMM*, 5(2005), 805-806

- E. Chung and B. Engquist. Convergence analysis of fully discrete finite volume methods for Maxwell's equations in non-homogeneous media.
*SIAM J. Numer. Anal.*, 43, 303-317, 2005

- B. Engquist, A.-K. Tornberg and R. Tsai. Discretization of Dirac delta functions in level set methods.
*J. Comput. Phys.*, 207, 28-51, 2005.

- B. Engquist and Y.-H. Tsai. Heterogeneous multiscale methods for stiff ordinary differential equations.
*Math. Comp.*, 74, 1707-1742, 2005

- E. Olsson and G. Kreiss. A conservative level set method for two phase flow.
*J Comp Phy*, vol 210(1), p225-246, 2005

- Katarina Blom and Axel Ruhe. Information Retrieval using a Krylov subspace method.
*SIAM Journal on Matrix Analysis and Applications*26:566-582, 2005.

- A. Szepessy, K.-S. Moon, R. Tempone och G. Zouraris, Convergence rates for adaptive weak approximation of stochastic differential equations.
*Stochastic Analysis and Applications*,23 (2005) 511-558

- A. Szepessy, A. Dzougoutov, K.-S. Moon, E. von Schwerin and R. Tempone, Adaptive Monte Carlo algorithms for stopped diffusion.
*Multiscale methods in science and engineering*, 59--88,*Lect. Notes Comput. Sci. Eng.*, 44, Springer, Berlin, 2005.

- A. Szepessy, K.-S. Moon, E. von Schwerin and R. Tempone, An Adaptive Algorithm for Ordinary, Stochastic and Partial Differential Equations.
*Recent advances in adaptive computation*, 325--343,*Contemp. Math.*, 383, Amer. Math. Soc., Providence, RI, 2005.

- I. Babuska, F. Nobile and R. Tempone, "Worst case scenario analysis for elliptic problems with uncertainty".
*Numer. Math., 101, 185–219*

- J. T. Oden, I. Babuska, F. Nobile, Y. Feng, R. Tempone, "Theory and Methodology for Estimation and Control of Errors Due to Modeling, Approximation, and Uncertainty".
*Computer Methods in Applied Mechanics and Engineering, Volume 194,Issues 2-5, No. 4, pp. 195-204*

- J. Hoffman, Computation of mean drag for bluff body problems using Adaptive DNS/LES,
*SIAM J. Sci. Comput., Vol 27(1), pp.184-207*, 2005.

- J. Hoffman, C. Johnson and S. Bertoluzza, Subgrid modeling for convection-diffusion-reaction in 1 space dimension using a Haar Multiresolution analysis,
*Comput. Meth. Appl. Mech. Engrg.,Vol 194, pp.19-44*, 2005.

- J. Jansson, C. Johnson, A. Logg, Computational Modeling of Dynamical Systems,
*Mathematical Models and Methods in Applied Sciences*, Vol 15, No. 3, 2005, pp. 471-481.

### 2004

- I. Daubechies, O. Runborg and W. Sweldens. Normal multiresolution approximation of curves.
*Constr. Approx.*, 20:399-463, 2004.

- J. Krishnan, O. Runborg and I. G. Kevrekidis, Bifurcation analysis of nonlinear reaction-diffusion problems using wavelet-based reduction techniques.
*Comput. Chem. Eng.*, 28:557-574, 2004.

- J.-D. Benamou, F. Collino and O. Runborg. Numerical microlocal analysis of harmonic wavefields.
*J. Comput. Phys.,*199:717-741, 2004.

- A.-K. Tornberg and B. Engquist. Numerical approximations of singular source terms in differential equations.
*J. Comput. Phys.*, 200, 462-488, 2004

- G. Kreiss and G. Efraimsson. Approximate solutions of slightly viscous conservation laws.
*Quart. Appl. Math*, vol 62, no 1, 2004

- I. Babuska, R. Tempone and G. Zouraris, "Galerkin finite element approximations of stochastic elliptic partial differential equations".
*SIAM Journal of Numerical Analysis Vol. 42, No. 2, pp.800-825*

- J. Hoffman, On duality based a posteriori error estimation in various norms and linear functionals for LES,
*SIAM J. Sci. Comput., Vol 26(1), pp.178-195*, 2004.

- M. Plexousakis and G.E. Zouraris. On the construction and analysis of high order locally conservative finite volume-type methods for one dimensional elliptic problems.
*SIAM Numer. Anal.*, vol.42, no. 3, pp. 1226-1260, 2004.

### 2003

- I. G. Kevrekidis, C. W. Gear, J. M. Hyman, P. G. Kevrekidis, O. Runborg and C. Theodoropoulos. Equation-free, coarse-grained multiscale computation: enabling microscopic simulators to perform system-level tasks.
*Commun. Math. Sci.*, 1:715-762, 2003.

- B. Engquist and O. Runborg. Computational high frequency wave propagation.
*Acta Numerica*, 12:181-266, 2003.

- W. E and B. Engquist. The heterogeneous multi-scale method.
*Commun. Math. Sci.*, 1, 87-133, 2003

- W. E and B. Engquist. Multi-scale Modeling and Computation.
*Notices of the AMS*, 50, 1062-1070, 2003

- A.-K. Tornberg and B. Engquist. Regularization techniques for numerical approximations of PDEs with singularities.
*J. of Sci. Comput.*, 19, 527-552, 2003

- W. E, B. Engquist and Z. Huang. Heterogeneous multi-scale method – a general methodology for multi-scale modelling.
*Phys. Rev. B*, 67, 092101, 2003

- A.-K. Tornberg and B. Engquist. The segment projection method for interface tracking.
*Commun. Pure Appl. Math.*, 56, 47-79, 2003

- M. Liefvendahl and G. Kreiss. Analytical and numerical Investigation of the resolvent for plane Couette flow.
*SIAM J Appl Math*, vol 63, no3, 2003

- M. Siklosi and G. Kreiss. Elimination of first order errors in time dependent shock calculations.
*SIAM J Num Anal*, vol 41, no 6, 2003

- M. Hanke and R. Lamour. Consistent initialization for nonlinear index-2 dae's: Large sparse systems in MATLAB.
*Numer. Algorithms*. 32(2003), 67-85

- M. Hanke. A new implementation of a BDF method within the method of lines.
*J. Comput. Meth. Sci. Engg.*Accepted for publication

- A. Szepessy, K.-S. Moon, R. Tempone, G. Zouraris, A varitational principle for adaptive approximation of ordinary differential equations.
*Numerische Mathematik*, 93 (2003), 131-152

- I. Babuska, K.-M. Liu and R. Tempone, "Solving Stochastic Partial Differential Equations Based on the Experimental Data".
*Mathematical Models and Methods in Applied Sciences Vol. 13, No. 3, 415-444*

- J. Hoffman, Subgrid modeling for convection-diffusion-reaction in 2 space dimensions using a Haar Multiresolution analysis,
*Math. Models Methods Appl. Sci., Vol 13(10), pp.1515-1536*, 2003.

### 2002

- F. Castella, B. Perthame and O. Runborg. High frequency limit of the Helmholtz equation II: Source on a general smooth manifold.
*Commun. Part. Diff. Eq.*, 27:607-651, 2002.

- B. Engquist, O. Runborg and A.-K. Tornberg. High frequency wave propagation by the segment projection method.
*J. Comput. Phys.*, 178:373-390, 2002.

- O. Runborg, C. Theodoropoulos and I. G. Kevrekidis. Effective bifurcation analysis: a time-stepper based approach.
*Nonlinearity*, 15:491-511, 2002.

- M. Liefvendahl and G. Kreiss. Bounds of the threshold amplitude for plane Couette flow.
*J Nonlinear Math Phys*, vol 9, no 3, 2002.

- A. Szepessy, Bachir B. Moussa, Scalar conservation laws with boundary conditions and rough data measure solutions.
*Methods and Applications of Analysis*, 9 (2002), 579-598.

- I.M. Gren, G. Destouni, and R. Tempone, "Cost effective policies for alternative distributions of stochastic water pollution".
*Journal of Environmental Management, 66, 145-157.*

- A.-K. Tornberg, "Multi-Dimensional Quadrature of Singular and Discontinuous Functions", BIT Numerical Mathemtics, 42:644-669, 2002

### 2001

- P.-O. Persson and O. Runborg. Simulation of a waveguide filter using wavelet-based numerical homogenization.
*J. Comput. Phys.,*166:361-382, 2001.

- G. Efraimsson, G. Kreiss and J. Nordström. Elimination of first order errors in shock calculations.
*SIAM J Num Anal*, 38, no 6,1986-1998, (2001)

- M. Liefvendahl and G. Kreiss. Stability of viscous shock waves for problems with non-symmetric viscosity matrices.
*SIAM J Math Anal*, 33, no 4, (2001)

- K. Gustavsson, J.Oppelstrup and J.Eiken, Consolidation of concentrated suspensions - shear and irreversible floc structure rearrangements,
*Computing and Visualization in Science*, 4:61-66, 2001.

- K. Gustavsson and J.Oppelstrup. Numerical 2D models of consolidation of dense flocculated suspensions,
*Journal of Engineering Mathematics*41:189-201, 2001.

- A. Szepessy, R. Tempone and G. Zouraris, Adaptive weak approximation of stochastic differntial equations.
*Comm. Pure Appl. Math*, 54, 1169-1214, 2001

- G. Zouraris. On the convergence of a linear two-step finite element method for the nonlinear Schrodinger equation.
*Mathematical Modelling and Numerical Analysis*, vol. 35, no. 3, pp. 389-405, 2001.

- J. Hoffman, Dynamic Subgrid Modeling for Time Dependent Convection-Diffusion-Reaction Equations with Fractal Solutions,
*International Journal for Numerical Methods in Fluids, Vol 40, pp.583-592*, 2001.

- G.D. Akrivis, V.A.Dougalis and G.E.Zouraris. Finite difference schemes for the "Parabolic" Equation in a variable depth environment with a rigid bottom boundary condition.
*SIAM Numer. Anal.*, vol.39, no.2, pp. 539-565, 2001.

### 2000

- O. Runborg. Some new results in multiphase geometrical optics.
*M2AN Math. Model. Numer. Anal.*, 34:1203-1231, 2000.

- A.-K. Tornberg and B. Engquist. A finite element based level-set method for multi-phase flow applications.
*Comput. and Visualization in Science*, 3, 93-101, 2000

- M. Hanke and L. Pu: Simulated annealing for the optimization of batch distillation processes.
*Comp. and Chem. Eng.. 24(2000)*, 1-8

- K. Gustavsson and J. Oppelstrup. Consolidation of concentrated suspensions - numerical simulations using a two-phase fluid model,
*Computing and Visualization in Science*3:39-45, 2000.

- A. Szepessy, High frequency asymptotics for 2D viscous shocks.
*Indiana Univ. Math. J.*49 (2000) no. 4.

- Axel Ruhe, A Rational Krylov algorithm for nonlinear matrix eigenvalue problems, Volume 268 of
*Zapiski Nauchnyh Seminarov POMI*, pages 176-180, 2000

## Conference Papers

### 2007

- B. Engquist, H. Holst and O. Runborg. Multiscale methods for the wave equation.Proceedings ICIAM 2007. To appear.

- M. Motamed and O. Runborg. Solution of High Frequency Wave Propagation Problems by a Fast Multiple-Patch Phase Space Method. Proceedings of Waves 2007, University of Reading, 102--104, 2007.

- M. Motamed and O. Runborg. A Wavefront Gaussian Beam Method for High-Frequency Wave Propagation. Proceedings of Waves 2007, University of Reading, 105--107, 2007.

- M. Hanke and M.C. Cabauatan-Villanueva: "On the simulation of the metabolism in mammalian cells using homogenization methods." In: Jean-Marc Petit and Oumnia Squalli, eds., Proceedings of the European Comsol Conference 2007, Grenoble, France, 40-46

- B. Engquist and L. Ying. Fast directional multilevel solver for integral formulations of wave scattering, Proceedings of Waves 2007, University of Reading, 63-64, 2007

### 2006

- A. Loubenets, B. Engquist and M.Hanke, A Non Body-fitted Finite Element Method for Elliptic Interface Problems, Proceedings International Conference on Numerical Analysis and Applied Mathematics 2006, Wiley-VCH, 2006

- M. Hanke and M. Strömgren. Degenerate hyperbolic systems in heat exchanger modeling: Analysis and numerical approximation. Oberwolfach Reports 3(2006), 1105-1106

- A. Szepessy, Atomistic and continuum models for phase change dynamics, Procedings ICM Madrid 2006.

- J. Hoffman, Simulating Drag Crisis for a Sphere Using Skin Friction Boundary Conditions,
*Proceedings ECCOMAS CFD*, 2006.

- J. Hoffman and C. Johnson, Irreversibility in Reversible Systems,
*HERMIS*, 2006.

### 2005

- M. Motamed and O. Runborg. A Fast Method for the Creeping Ray Contribution to Scattering Problems. Proceedings 2nd Conference on Mathematical Modeling of Wave Phenomena, Vaxjo, Sweden, 2005.

- A.Jaun, E.R. Tracy, A.N. Kaufman,
*Amplitude and Phase for Ray Splitting in Linear Wave Conversion*, conference, appeared, Proc. Am. Phys. Soc. Conf. DPP, Denver (2005)

- A.Jaun, E.R. Tracy, A.N. Kaufman,
*Amplitude and Phase for Ray Splitting in Linear Wave Conversion*, conference, appeared, Proc. Am. Phys. Soc. Conf. DPP, Denver (2005)

- O. Runborg. "Introduction to normal multiresolution analysis." In B. Engquist, P. Lötstedt, O. Runborg, editors,
*Multiscale Methods in Science and Engineering,*pages 205-224,volume 44 of*Lecture Notes in Computational Science and Engineering,*Heidelberg, 2005. Springer Verlag.

- R. Sharp, Y.-H. Tsai and B. Engquist. Multiple time scale methods for the inverted pendulum problem, Proceedings of Conference on Multiscale Methods in Science and Engineering, Lecture Notes in Computational Science and Engineering, Springer Verlag, 44, 233-244, 2005

- W. E. and B. Engquist. The Heterogeneous Multi-Scale Method for Homogenization Problems, Proceedings of Conference on Multiscale Methods in Science and Engineering, Lecture Notes in Computational Science and Engineering, Springer Verlag, 44, 71-92, 2005

- B. Engquist. Multi-scale modeling, Proc. from Perspective in Analysis, Carleson 75, Math. Phys. studies 27, Springer Verlag, 51-61, 2005

- I. Babuska, F. Nobile and R. Tempone, "Worst-case scenario analysis for elliptic PDE's with uncertainty",
*Proceedings of the EURODYN conference, Paris, September 4-7, 2005*.

- J. Hoffman, Weak Uniqueness of the Navier-Stokes Equations and Adaptive Turbulence Simulation,
*Leslie Fox Prize Meeting, University of Dundee*, 2005.

### 2004

- S. Hagdahl and B. Engquist. Computation of smooth surface diffraction for industrial applications, Proceedings of EMB04, 82-89, 2004

- D. S. Henningson and G. Kreiss. Threshold amplitudes in subcritical shear flows. Nonlinear stability bounds. Proceedings of the IUTAM Symposium Non-Uniqueness of Solutions to the Navier-Stokes Equations and their Connection with Laminar-Turbulent Transition, Bristol, August 2004

- G. Kreiss, H.-O. Kreiss and J. Lorenz. Stability of viscous shocks on finite intervals. Proceedings of 10th international conference on Hyperbolic problems, Osaka, September 2004

- K. Gustavsson, B. Sjögreen and R.L. Gudmundsson, A Model Equation for Peak Formation in Two-Phase Flow, Proceedings of the Tenth International Conference on Hyperbolic Problems, Osaka, Japan, September 2004.

- Axel Ruhe, Rational Krylov for Large Nonlinear Eigenproblems,
*Talk given at PARA 04, Copenhagen June 21, 2004 SPRINGER Lecture Notes in Computer Science*, Volume 3732 pp. 357-363, 2006.

### 2003

- D. Appelö and G. Kreiss. Discretely Nonreflecting Boundary Conditions for Higher order Centered Schemes for Wave equations. In Heikkola, Neittaanmäki, Cohen, Joly ed.
*Mathematical and Numerical Aspects of Wave Propagation*, Proceedings Waves2003, Springer, 2003

- G. Kreiss and H.-O. Kreiss. A Half Plane Problem Related to the Stability of Viscous Shock Waves. In Heikkola, Neittaanmäki, Cohen, Joly ed.
*Mathematical and Numerical Aspects of Wave Propagation*, Proceedings Waves2003, Springer, 2003

- M. Siklosi and G. Kreiss. Elimination of First Order Errors in Time Dependent Shock Calculations. In Heikkola, Neittaanmäki, Cohen, Joly ed,
*Mathematical and Numerical Aspects of Wave Propagation*, Proceedings Waves2003, Springer, 2003

- K. Gustavsson and B. Sjögreen, Numerical Study of a Viscous Consolidation Model,
*Hyperbolic Problems: Theory, Numerics, Applications*, Proceedings of the Ninth International Conference on Hyperbolic Problems, Pasadena, USA, 2002, Springer-Verlag, 2003.

- J. Hoffman and C Johnson, Adaptive finite element methods for turbulent flow,
*Proceedings of ENUMATH 2003 the 5th European conference on Numerical Mathematics and Advanced Applications Prague*, 2003.

### 2002

- B. Engquist and O. Runborg. Projection generated homogenization. In N. Antonic, C. J. van Duijn, W. Jäger, and A. Mikelic, editors,
*Multiscale Problems in Science and Technology,*pages 129-150, Springer-Verlag, 2002.

- B. Engquist and A.-K. Tornberg. A finite element based level-set method for multi-phase flow, Proceedings of Conference on Progress in Numerical Solutions of Partial Differential Equations, Arcachon 1998, World Scientific Publ., 86-110, 2002

- S. Hagdahl and B. Engquist. Numerical techniques for mixed high-low frequency EM-problems, Proceedings of RVK02, 18-22, 2002

- D. Appelö and G. Kreiss. Evaluation of the Well-Posed Perfectely Matched Layer for Advective Acoustics. Proceedings of 9th international conference on Hyperbolic problems in Pasadena, 2002

- M. Kupianen and G. Kreiss. Effects of Viscosity on a Shock Wave Solution of the Euler Equations. Proceedings of 9th international conference on Hyperbolic problems in Pasadena, 2002

- J. Hoffman and C. Johnson, Adaptive multiscale computational modeling of complex incompressible fluid flow,
*conference proceedings of WCCM Fith World Congress on Computational Mechanics, Vienna*, 2002.

### 2001

- B. Engquist and O. Runborg. Wavelet-based numerical homogenization with applications. In T.J. Barth, T.F. Chan and R. Haimes, editors,
*Multiscale and Multiresolution Methods: Theory and Applications,*pages 97-148, volume 20 of*Lecture Notes in Computational Science and Engineering,*Heidelberg, 2001. Springer Verlag.

- G. Efraimsson, J. Nordström and G. Kreiss. Artificial Dissipation and Accuracy Downstream of Slightly Viscous Shocks. 15th AIAA CFD Conference, paper 2001-2608, 2001.

- Katarina Blom and Axel Ruhe. Information retrieval using very short Krylov sequences. In M.W. Berry, editor,
*Computational Information Retrieval*, volume 106 of Proceedings in Applied Mathematics, pages 41-56. SIAM, Philadelphia, 2001

- J. Hoffman and C. Johnson, Adaptive finite element methods for incompressible fluid flow,
*proceedings/lecture notes of Nasa/VKI Lecture series: Error Estimation and Solution Adaptive Discretization in Computational Fluid Dynamics*, 2001.

- J. Hoffman, C. Johnson, and A. Logg, Topics in adaptive computational methods for differential equations,
*conference proceedings of Congreso de Ecuaciones Diferenciales y Aplicaciones Salamanca*, 2001.

- J. Hoffman, Dynamic subgrid modeling for time dependent convection-diffusion-reaction equations with fractal solutions,
*conference proceedings of ICFD 2001: International Conference for Numerical Methods in Fluids*, 2001.

### 2000

- A.-K. Tornberg and B. Engquist. Interface tracking in two-phase flows, Multi-phase problems – state of the art, Proceedings of Conference Algoritmy2000. Springer-Verlag, 58-66, 2000

- A.-K. Tornberg and B. Engquist. Finite element based methods for interface flow simulations, Proceedings of Conference ENUMATH99, World Science Publ., 251-258, 2000

- G. Kreiss and M. Siklosi. Proving Existence of Solutions of Nonlinear Equations Using Numerical Approximations.
*Hyperbolic problems, eighth international conference in Magdeburg*, ed Freistüler and Warnecke, Birkhäuser, 2000.

- M. Liefvendahl and G. Kreiss. Examples of Unstable Shock Waves.
*Hyperbolic problems, eighth international conference in Magdeburg*, ed Freistüler and Warnecke, Birkhäuser, 2000.

- J. Hoffman, Dynamic Subgrid Modeling for Scalar Convection-Diffusion-Reaction Equations with Fractal Coefficients,
*conference proceedings of YES 2000: Yosemite Educational Symposium on Multiscale and Multiresolution Methods*, 2000.

## Book Chapters

- B. Engquist and O. Runborg. Wavelet-based Numerical Homogenization. Results from Program on Highly Oscillatory Problems. Isaac Newton Institute for Mathematical Sciences, Cambridge, UK, 2008.

- M. Motamed and O. Runborg. Asymptotic approximations of high frequency wave propagation problems. Results from Program on Highly Oscillatory Problems. Isaac Newton Institute for Mathematical Sciences, Cambridge, UK, 2008.

- J. Hoffman and C. Johnson, Computability and Adaptivity in CFD,
*Encyclopedia of Computational Mechanics*, Eds. E. Stein, R. de Borst and T.J.R. Hughes, 2007.

- J. Hoffman and C Johnson, Adaptive finite element methods for turbulent flow,
*Numerical Mathematics And Advanced Applications Proceedings of ENUMATH 2003 the 5th European conference on Numerical Mathematics and Advanced Applications; Prague, August 2003*, Springer, 2004.

- J. Hoffman and C. Johnson, Adaptive DNS/LES: a New Agenda in CFD, in
*Finite Element Methods: 1970s and beyond*, CIMNE, 2004.

- J. Hoffman and C. Johnson, Computability and Adaptivity in CFD,
*Encyclopedia of Computational Mechanics*, Eds. E. Stein, R. de Borst and T.J.R. Hughes, 2004.

- J. Hoffman and C. Johnson, Adaptive finite element methods for incompressible fluid flow,
*Error Estimation and Solution Adaptive Discretization in Computational Fluid Dynamics, Eds. T. J. Barth and H. Deconinck, Lecture Notes in Computational Science and Engineering, Springer-Verlag Publishing, Heidelberg*, 2002.

- J. Hoffman, Dynamic Subgrid Modeling for Scalar Convection-Diffusion-Reaction Equations with Fractal Coeffcients,
*Multiscale and Multiresolution Methods: Theory and Applications, Eds. T. J. Barth, T. Chan and R. Haimes, Lecture Notes in Computational Science and Engineering, Springer-Verlag Publishing, Heidelberg*, 2001.

- B. Engquist and G. Golub. From numerical analysis to computational science, Chapter in Mathematics Unlimited: 2001 and Beyond, Springer-Verlag, 433-448, 2000

## Books

- J. Hoffman and C. Johnson,
*Computational Turbulent Incompressible Flow: Applied Mathematics Body and Soul Vol 4, Springer-Verlag Publishing*, 2007.

- B. Engquist, P. Lötstedt and O. Runborg (editors).
*Multiscale Methods in Science and Engineering*Lecture Notes in Computational Science and Engineering 44, Springer-Verlag, 2005.

- J. Hoffman, C. Johnson and A. Logg,
*Dreams of Calculus: Perspectives on Mathematics Education, Springer-Verlag Publishing*, 2004.

- B. Engquist and W. Schmidt (editors).
*Mathematics Unlimited: 2001 and Beyond*, Springer-Verlag, 2000

- B. Engquist, L. Johnsson, M. Hammill and F. Short (editors).
*Simulation and Visualization on the Grid, Proceedings PDC Seventh Annual Conference*, Lecture Notes in Computational Science and Engineering, Springer-Verlag, Vol 13, 2000

- Z. Bai, J. Demmel, J. Dongarra, A. Ruhe, and H. van der Vorst, editors.
*Templates for the solution of Algebraic Eigenvalue Problems: A Practical Guide.*SIAM, Philadelphia, 2000.

## Technical Reports

- M. Hanke and T. Reis. " The perturbation and ADAE index of a degenerated hyperbolic system modelling a heat exchanger." Berlin: Technical University, DFG Research Center MATHEON, 2007 (Technical Report 394-2007). Submitted

- M. Hanke and M.C. Cabauatan-Villanueva. "Analytical And Numerical Approximation of Effective Diffusivities in The Cytoplasm of Biological Cells." Stockholm: Royal Inst. of Technology 2007 (Report TRITA-NA-2007:6)

- M. Hanke and A. Loubenets. "An immersed finite element method and its convergence for elliptic interface problems with discontinuous coefficients and singular sources." Stockholm: Royal Inst. of Technology 2007 (Report TRITA-NA-2007:3). Submitted

- A. Loubenets and M. Hanke: "A non-conforming finite element method for interface Stokes problems and its application to two-phase Rayleigh-Taylor instability with solid obstacles." Stockholm: Royal Inst. of Technology 2007 (Report TRITA-NA-2007:4). Submitted

- M. Hanke. "Benchmarking Femlab 3.1i: Solid Structural Mechanics." Stockholm: Royal Inst. of Technology 2005 (Report TRITA-NA-0546)

- K. Gustavsson, B. Sjögreen, and R.L. Gudmundsson, Peak Formation in the Two-Phase Equations:Non-Existence of Shocks, Department of Numerical Analysis and Computing Science, Royal Institute of Technology (KTH), Stockholm, Sweden, TRITA-NA-0537, 2005.

- E. Olsson and G. Kreiss. A Conservative Level Set Method with Artificial Compression for Two Phase Flow. TRITA-NA-0418, submitted, (2004)

- G. Kreiss, H.-O. Kreiss and J. Lorenz. Stability of Viscous Shock profiles: Resolvent Estimates. TRITA-NA-0421, (2004)

- M. Hanke. A note on the consistent initialization for nonlinear index-2 differential-algebraic equations in Hessenberg form. PSCI report; 04:02

- M. Hanke. Benchmarking Femlab 3.0a: Laminar Flows in 2D. PSCI report 04:01

- G. Kreiss, H.-O. Kreiss and J. Lorenz. Stability of Viscous Shocks on Finite Intervalls. TRITA-NA-0422, (2004)

- D. Appelö and G. Kreiss. Stabilized local Non-reflecting Boundary Conditions for high order methods. TRITA-NA-0325, (2003)

- P.-O. Åsen and G. Kreiss. A Rigorous Resolvent Estimate for Plane Couette Flow. TRITA- NA-0330, submitted, (2003)

- M. Hanke. Preconditioning strategies for multiphysics applications: Some problems. PSCI report; 02:03

- K. Gustavsson and B. Sjögreen, Numerical Methods for One Dimensional Consolidation Models, Department of Numerical Analysis and Computing Science, Royal Institute of Technology (KTH), Stockholm, Sweden, TRITA-NA-0143, 2002.

- M. Plexousakis and G. E. Zouraris. High order locally conservative finite volume-type approximations of one dimensional elliptic problems. TRITA-NA-0138, (2001)

- M. Kupianen and G. Kreiss. Stability investigation of a shock wave solution of the Euler equations. TRITA-NA-0124, (2001)

- C. Johansson, G. Kreiss, M. Siklosi, M. Liefvendahl and J. Nordström. Stable and accurate Boundary Conditions for Aerodynamic and Aeroacoustic Calculations. TRITA-NA-0015, (2000)

## Software

- J. Hoffman, J. Jansson, M. Nazarov, M. Stöckli. Unicorn: unified continuum mechanics solver. http://www.fenics.org/wiki/Unicorn.

- J. Hoffman, J. Jansson, Anders Logg and Garth Wells. DOLFIN: PDE problem solving environment. http://www.fenics.org/wiki/DOLFIN.