On finite element schemes for Vlasov-Maxwell system and Schrödinger equation
Doctoral thesis, 2017

This thesis treats finite element schemes for two kind of problems, the Valsov-Maxwellsystem and the nonlinear Schrödinger equation. We study streamline diffusion schemes applied for numerical solution of the one and one-half dimensional relativistic Vlasov-Maxwell system. The study is made both in a priori and a posteriori settings. In the a priori setting we derive stability estimates and prove optimal convergence rates, due to the maximal available regularity of the exact solution. In addition to this we also prove existence and uniqueness of the numerical solution. In the a posteriori setting we use dual problems to prove error estimates in L_\infty (H^{-1}) norm. For the Maxwell equation we also prove error estimates in H^{-1} (H^{-1}) norms. Further more we study a hp-version of the streamline diffusion scheme for thethree dimensional Vlasov-Maxwell system in an a priori setting. A Nitsche type scheme is also introduced and analyzed for Maxwell's equations. For the nonlinear Schrödinger equation a two level time discretization is used. Here we derive a priori error estimates both in L_2 and H^1 norms.

a posteriori error analysis

Nonlinear Schrödinger equation

Streamline diffusion

Vlasov-Maxwell

Nitsche scheme

hp-scheme

a priori error analysis

Pascal
Opponent: Francis Filbet, Institut de Mathématiques de Toulouse, Université Toulouse III & Institut Universitaire de France

Author

Christoffer Standar

Chalmers, Mathematical Sciences

Asadzadeh, M, Standar, C. A posteriori error estimates for the one and one-half Dimensional Relativistic Vlasov-Maxwell system.

Asadzadeh, M, Kowalczyk, P, Standar, C. On hp-Streamline Diffusion and Nitsche schemes for the Relativistic Vlasov-Maxwell System

Asadzadeh, M, Standar, C. Approximating the nonlinear Schrödinger equation by a two level linearly implicit finite element method

Subject Categories

Computational Mathematics

Mathematical Analysis

ISBN

978-91-7597-669-3

Doktorsavhandlingar vid Chalmers tekniska högskola. Ny serie: 4350

Publisher

Chalmers University of Technology

Pascal

Opponent: Francis Filbet, Institut de Mathématiques de Toulouse, Université Toulouse III & Institut Universitaire de France

More information

Created

11/22/2017