Stability Analysis of Discontinuous Galerkin Approximations to the Elastodynamics Problem

被引：26

作者：

Antonietti, Paola F. ^{[5
]}

de Dios, Blanca Ayuso ^{[2
,3
,4
]}

Mazzieri, Ilario ^{[5
]}

Quarteroni, Alfio ^{[1
,5
]}

机构：

[1] Ecole Polytech Fed Lausanne, CMCS, Stn 8, CH-1015 Lausanne, Switzerland

[2] Tech Univ Hamburg, Inst Math, Schwarzenberg Campus 3, D-21073 Hamburg, Germany

[3] CNR, IMATI, I-27100 Pavia, Italy

[4] Univ Bologna, Dipartimento Matemat, Piazza Porta San Donato 5, I-40126 Bologna, Italy

[5] Politecn Milan, MOX, Dipartimento Matemat, Piazza Leonardo da Vinci 32, I-20133 Milan, Italy

来源：

JOURNAL OF SCIENTIFIC COMPUTING | 2016年 / 68卷 / 01期

关键词：

Discontinuous Galerkin methods; Elastodynamics equation; Stability and error analysis; SPECTRAL-ELEMENT METHOD; ELASTIC-WAVE PROPAGATION; UNSTRUCTURED MESHES; SIMULATION; EARTHQUAKE; EQUATIONS; 2D;

D O I：

10.1007/s10915-015-0132-2

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider semi-discrete discontinuous Galerkin approximations of both displacement and displacement-stress formulations of the elastodynamics problem. We prove the stability analysis in the natural energy norm and derive optimal a-priori error estimates. For the displacement-stress formulation, schemes preserving the total energy of the system are introduced and discussed. We verify our theoretical estimates on two and three dimensions test problems.

引用

页码：143 / 170

页数：28

共 54 条

[1]

Adams R., 2003, SOBOLEV SPACES

[2]

[Anonymous], 562013 MOX

[3] Non-conforming high order approximations of the elastodynamics equation [J].

Antonietti, P. F. ;

Mazzieri, I. ;

Quarteroni, A. ;

Rapetti, F. .

COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 2012, 209 :212-238

[4] High order discontinuous Galerkin methods on simplicial elements for the elastodynamics equation [J].

Antonietti, Paola F. ;

Marcati, Carlo ;

Mazzieri, Ilario ;

Quarteroni, Alfio .

NUMERICAL ALGORITHMS, 2016, 71 (01) :181-206

[5] Unified analysis of discontinuous Galerkin methods for elliptic problems [J].

Arnold, DN ;

Brezzi, F ;

Cockburn, B ;

Marini, LD .

SIAM JOURNAL ON NUMERICAL ANALYSIS, 2002, 39 (05) :1749-1779

[6] AN INTERIOR PENALTY FINITE-ELEMENT METHOD WITH DISCONTINUOUS ELEMENTS [J].

ARNOLD, DN .

SIAM JOURNAL ON NUMERICAL ANALYSIS, 1982, 19 (04) :742-760

[7] Locking-free Reissner-Mindlin elements without reduced integration [J].

Arnold, Douglas N. ;

Brezzi, Franco ;

Falk, Richard S. ;

Marini, L. Donatella .

COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 2007, 196 (37-40) :3660-3671

[8]

Brenner SC, 2004, MATH COMPUT, V73, P1067

[9] Poincare-Friedrichs inequalities for piecewise H1 functions [J].

Brenner, SC .

SIAM JOURNAL ON NUMERICAL ANALYSIS, 2003, 41 (01) :306-324

[10] WAVE-PROPAGATION SIMULATION IN AN ELASTIC ANISOTROPIC (TRANSVERSELY ISOTROPIC) SOLID [J].

CARCIONE, JM ;

KOSLOFF, D ;

KOSLOFF, R .

QUARTERLY JOURNAL OF MECHANICS AND APPLIED MATHEMATICS, 1988, 41 :319-345

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