Discontinuous Galerkin finite element methods for dynamic linear solid viscoelasticity problems

被引：40

作者：

Riviere, Beatrice

Shaw, Simon

Whiteman, J. R. ^{[1
]}

机构：

[1] Brunel Univ, Brunel Inst Computat Math, Uxbridge UB8 3PH, Middx, England

[2] Univ Pittsburgh, Dept Math, Computat Math Grp, Pittsburgh, PA 15260 USA

来源：

NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS | 2007年 / 23卷 / 05期

关键词：

viscoelasticity; finite element method; discontinuous Galerkin method; a priori error estimates;

D O I：

10.1002/num.20215

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider the usual linear elastodynamics equations augmented with evolution equations for viscoelastic internal stresses. A fully discrete approximation is defined, based on a spatially symmetric or non-symmetric interior penalty discontinuous Galerkin finite element method, and a displacement-velocity centred difference time discretisation. An a priori error estimate is given but only the main ideas in the proof of the error estimate are reported here due to the large number of (mostly technical) estimates that are required. The full details are referenced to a technical report. (c) 2007 Wiley Periodicals, Inc.

引用

页码：1149 / 1166

页数：18

共 50 条

[31] AUTOMATIC SYMBOLIC COMPUTATION FOR DISCONTINUOUS GALERKIN FINITE ELEMENT METHODS
Houston, Paul
Sime, Nathan
SIAM JOURNAL ON SCIENTIFIC COMPUTING, 2018, 40 (03): : C327 - C357
[32] Port-Hamiltonian discontinuous Galerkin finite element methods
Kumar, Nishant
van der Vegt, J. J. W.
Zwart, H. J.
IMA JOURNAL OF NUMERICAL ANALYSIS, 2024,
[33] HpGEM - A software framework for discontinuous galerkin finite element methods
Pesch, Lars
Bell, Alexander
Sollie, Henk
Ambati, Vijaya R.
Bokhove, Onno
Van der Vegt, Jaap J. W.
ACM TRANSACTIONS ON MATHEMATICAL SOFTWARE, 2007, 33 (04):
[34] Implicit and explicit discontinuous galerkin finite element procedures for linear and nonlinear structural dynamic analysis
Wiberg, NE
Li, XD
COMPUTATIONAL PLASTICITY: FUNDAMENTALS AND APPLICATIONS, PTS 1 AND 2, 1997, : 224 - 238
[35] Rapid non-linear finite element analysis of continuous and discontinuous Galerkin methods in MATLAB
O'Sullivan, S.
Bird, R. E.
Coombs, W. M.
Giani, S.
COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2019, 78 (09) : 3007 - 3026
[36] LOW-ORDER DISCONTINUOUS PETROV-GALERKIN FINITE ELEMENT METHODS FOR LINEAR ELASTICITY
Carstensen, C.
Hellwig, F.
SIAM JOURNAL ON NUMERICAL ANALYSIS, 2016, 54 (06) : 3388 - 3410
[37] hp-discontinuous Galerkin finite element methods for hyperbolic problems:: error analysis and adaptivity
Houston, P
Senior, B
Süli, E
INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, 2002, 40 (1-2) : 153 - 169
[38] Coupling of finite element and plane waves discontinuous Galerkin methods for time-harmonic problems
Gaborit, M.
Dazel, O.
Goransson, P.
Gabard, G.
INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, 2018, 116 (07) : 487 - 503
[39] DISCONTINUOUS GALERKIN FINITE-ELEMENT METHODS FOR 2ND-ORDER HYPERBOLIC PROBLEMS
JOHNSON, C
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 1993, 107 (1-2) : 117 - 129
[40] A NEW ERROR ANALYSIS FOR DISCONTINUOUS FINITE ELEMENT METHODS FOR LINEAR ELLIPTIC PROBLEMS
Gudi, Thirupathi
MATHEMATICS OF COMPUTATION, 2010, 79 (272) : 2169 - 2189

← 1 2 3 4 5 →