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

被引：29
|
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
相关论文
共 50 条
  • [1] A SPACE-TIME DISCONTINUOUS GALERKIN METHOD FOR FIRST ORDER HYPERBOLIC SYSTEMS
    Zhang, Tie
    Liu, Jingna
    [J]. JOURNAL OF THE KOREAN MATHEMATICAL SOCIETY, 2014, 51 (04) : 665 - 678
  • [2] Discontinuous Galerkin methods for first-order hyperbolic problems
    Brezzi, F
    Marini, LD
    Suli, E
    [J]. MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES, 2004, 14 (12): : 1893 - 1903
  • [3] Space-Time Discontinuous Galerkin Methods for Weak Solutions of Hyperbolic Linear Symmetric Friedrichs Systems
    Corallo, Daniele
    Doerfler, Willy
    Wieners, Christian
    [J]. JOURNAL OF SCIENTIFIC COMPUTING, 2023, 94 (01)
  • [4] Space-Time Discontinuous Galerkin Methods for Weak Solutions of Hyperbolic Linear Symmetric Friedrichs Systems
    Daniele Corallo
    Willy Dörfler
    Christian Wieners
    [J]. Journal of Scientific Computing, 2023, 94
  • [5] A space-time Trefftz discontinuous Galerkin method for the acoustic wave equation in first-order formulation
    Moiola, Andrea
    Perugia, Ilaria
    [J]. NUMERISCHE MATHEMATIK, 2018, 138 (02) : 389 - 435
  • [6] Superconvergence of the space-time discontinuous Galerkin method for linear nonhomogeneous hyperbolic equations
    Hu, Hongling
    Chen, Chuanmiao
    Hu, Shufang
    Pan, Kejia
    [J]. CALCOLO, 2021, 58 (02)
  • [7] Superconvergence of the space-time discontinuous Galerkin method for linear nonhomogeneous hyperbolic equations
    Hongling Hu
    Chuanmiao Chen
    Shufang Hu
    Kejia Pan
    [J]. Calcolo, 2021, 58
  • [8] Space-Time Discontinuous Galerkin Methods for Linear Hyperbolic Systems and the Application to the Forward Problem in Seismic Imaging
    Doerfler, Willy
    Wieners, Christian
    Ziegler, Daniel
    [J]. FINITE VOLUMES FOR COMPLEX APPLICATIONS IX-METHODS, THEORETICAL ASPECTS, EXAMPLES, FVCA 9, 2020, 323 : 477 - 485
  • [9] A SPACE-TIME DISCONTINUOUS GALERKIN METHOD FOR LINEAR HYPERBOLIC PDE'S WITH HIGH FREQUENCIES
    Toprakseven, Suayip
    [J]. COMMUNICATIONS FACULTY OF SCIENCES UNIVERSITY OF ANKARA-SERIES A1 MATHEMATICS AND STATISTICS, 2020, 69 (01): : 213 - 231
  • [10] Space-time discontinuous Galerkin method for linear elastodynamics
    Aksoy, H. G.
    Senocak, E.
    [J]. JOURNAL OF AEROSPACE ENGINEERING, 2007, 20 (02) : 128 - 131
12345