Space-Time Discontinuous Galerkin Discretizations for Linear First-Order Hyperbolic Evolution Systems

被引：32
作者：
Doerfler, Willy [1 ]
Findeisen, Stefan [1 ]
Wieners, Christian [1 ]
机构：
[1] KIT, Inst Angew & Numer Math, D-76049 Karlsruhe, Germany
来源：
COMPUTATIONAL METHODS IN APPLIED MATHEMATICS | 2016年 / 16卷 / 03期
关键词：
Space-Time Methods; Discontinuous Galerkin Finite Elements; Linear Hyperbolic Systems; Transport Equation; Wave Equation; Maxwell's Equations; PARALLEL; INTEGRATION; PARAREAL;
D O I：
10.1515/cmam-2016-0015
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We introduce a space-time discretization for linear first-order hyperbolic evolution systems using a discontinuous Galerkin approximation in space and a Petrov-Galerkin scheme in time. We show well-posedness and convergence of the discrete system. Then we introduce an adaptive strategy based on goal-oriented dual-weighted error estimation. The full space-time linear system is solved with a parallel multilevel preconditioner. Numerical experiments for the linear transport equation and the Maxwell equation in 2D underline the efficiency of the overall adaptive solution process.
引用
收藏
页码：409 / 428
页数：20
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