Some Papers and Lecture Notes

Molecular Dynamics

The classical limit of quantum observables in conservation laws of fluid dynamics with Mattias Sandberg, arXiv:1702.04368

Canonical quantum observables for molecular systems approximated by ab initio molecular dynamics, with Aku Kammonen, Mattias Sandberg, arXiv:1611.04909

Computational error estimates for Born-Oppenheimer molecular dynamics with nearly crossing potential surfaces, with Christian Bayer, Ashraful, Kadir, Hakon Hoel, Petr Plechac and Mattias Sandberg, arxiv:1305.3330v5

How accurate is molecular dynamics?, with Christian Bayer, Hakon Hoel, Petr Plechac, Mattias Sandberg and Raul Tempone, arXiv:1104.0953v1.

A stochastic phase-field model determined from molecular dynamics, with Erik von Schwerin, M2AN Math. Model. Numer. Anal. 44 (2010), no. 4, 627-646

Langevin molecular dynamics derived from Ehrenfest dynamics, Math. Models Methods Appl. Sci. 21 (2011), no. 11, 2289-2334. arXiv:0712.3656

Stochastic Differential Equations

Computable error estimates for finite element approximations of elliptic partial differential equations with rough stochastic data , with Eric Joseph Hall, Hakon Hoel, Mattias Sandberg, Raul Tempone, arXiv:1510.02708, SIAM J. Sci. Comput. 38(6) A3773-A3807 (2016)

T. Bjork, A. Szepessy R. Tempone and G.E. Zouraris "Monte Carlo Euler approximations of HJM term structure financial models", BIT Numerical Mathematics DOI 10.1007/s10543-012-0410-4, 2012

Adaptive weak approximation of reflected and stopped diffusion, with Christian Bayer and Raul Tempone, Monte Carlo Methods and Appl, 16 (2010).

Adaptive weak approximation of diffusions with jumps, with Ernesto Mordecki, Raul Tempone and Georgios Zouraris, SIAM Journal on Numerical Analysis (Vol.46, No.4) 2008.

Atomistic and continuum models for phase change dynamics procedings ICM Madrid 2006.

Stochastic hydrodynamical limits of particle systems with Markos Katsoulakis, Communications in Mathematical Sciences (CMS) Vol 4, No. 3, September 2006

Convergence rates for adaptive weak approximation of stochastic differential equations, with Kyoung-Sook Moon, Raul Tempone och Georgios Zouraris, Stochastic Analysis and Applications,23 (2005) 511-558. ps,

Adaptive Monte Carlo algorithms for stopped diffusion, with Anna Dzougoutov, Kyoung-Sook Moon, Erik von Schwerin and Raul Tempone, Multiscale methods in science and engineering, 59--88, Lect. Notes Comput. Sci. Eng., 44, Springer, Berlin, 2005.

An Adaptive Algorithm for Ordinary, Stochastic and Partial Differential Equations, with Kyoung-Sook Moon, Erik von Schwerin and Raul 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.

Adaptive weak approximation of stochastic differntial equations, .pdf, with Raul Tempone and Georgois Zouraris, Comm. Pure Appl. Math, 54, 1169-1214, 2001

Optimal Control

An a posteriori error estimate for Symplectic Euler approximation of optimal control problems with Jesper Karlsson, Stig Larsson, Mattias Sandberg, Raul Tempone, arXiv:1407.8330

Symplectic Pontryagin approximation for optimal design with Jesper Carlsson and Mattias Sandberg, M2AN Math. Model. Numer. Anal. 43 (2009), no. 1, 3--32.

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

Numerics

Convergece rates of an adaptive dual weighted residual finite element algorithm, with Kyoung-Sook Moon, Erik von Schwerin and Raul Tempone, BIT Numerical Mathematics (2006) 46, 367-407.

A varitational principle for adaptive approximation of ordinary differential equations, with Kyoung-Sook Moon, Raul Tempone och Georgios Zouraris, Numerische Mathematik, 93 (2003), 131-152.

Convergence rates for adaptive approximation of ordinary differential equations, with Kyoung-Sook Moon, Raul Tempone och Georgios Zouraris, Numerische Mathematik, 93 (2003), 99-129.

On the convergence of multigrid methods for flow problems , with Klas Samuelsson and Ingemar Persson, Electron. Trans. Numer. Anal. 8 (1999), 46-87.

On the stability of finite element methods for shock waves, Comm. Pure Appl. Math., 45 (1992), 923-946.

Anisotropic refinement algorithms for finite elements, with Jonathan Goodman and Klas Samuelsson.

Adaptive finite element methods for conservation laws based on a posteriori error estimates, with Claes Johnson, Comm. Pure Appl. Math., (1995), 199-234.

Partial Differential Equations

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

Dynamics and stability of a weak detonation wave, Comm. Math. Phys. 202 (1999) no. 3, 547-569.

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

Nonlinear stability of viscous shock waves, with Zhouping Xin, Arch. Rat. Mech. Anal., 122 (1993), 53-103.

Stability of rarefaction waves in viscous media, with Kevin Zumbrun, Arch. Rat. Mech. Anal., 133 (1996),249-298.

On the stability of Broadwell shocks, Proceedings of the International Conference on Nonlinear Evolution Partial Differential Equations, Beijing 1993, PR China, International Press.

Lecture notes

Stability of nonlinear waves in viscous media and numerics, in "Analysis of Systems of Conservation Laws", Edited by H. Freist\"uhler, Chapman and Hall/CRC Monograph series in Pure and Applied Mathematics, 1999.

Hyperbolic differential equations and adaptive numerics, with K.-S. Moon, R. Tempone and G. Zouraris, in "Theory and Numerics of Differential Equations". Edited by J. F. Blowey, J. P. Coleman and A. Craig, Springer-Verlag, 2001.