Analysis of a Staggered Discontinuous Galerkin Method for Linear Elasticity

被引：0
作者：
Jeonghun J. Lee
Hyea Hyun Kim
机构：
[1] University of Oslo,Department of Mathematics
[2] Kyung Hee University,Department of Applied Mathematics
来源：
Journal of Scientific Computing | 2016年 / 66卷
关键词：
Discontinuous Galerkin method; Linear elasticity; Error analysis; Weak symmetry; 65N30; 65N12;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
We develop a staggered discontinuous Galerkin method for linear elasticity problems and prove its a priori error estimates. In our variational formulation the symmetry of the stress tensor is imposed weakly via Lagrange multipliers but the resulting numerical stress tensor is strongly symmetric. Optimal a priori error estimates are obtained and the error estimates are robust in nearly incompressible materials. Numerical experiments illustrating our theoretical analysis are included.
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页码：625 / 649
页数：24
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[11]  
Gupta CP(2009)Optimal discontinuous Galerkin methods for the acoustic wave equation in higher dimensions SIAM J. Numer. Anal. 47 3820-3848
[12]  
Arnold DN(2010)A new elasticity element made for enforcing weak stress symmetry Math. Comp. 79 1331-1349
[13]  
Falk RS(2013)Superconvergent HDG methods for linear elasticity with weakly symmetric stresses IMA J. Numer. Anal. 33 747-770
[14]  
Winther R(1997)Dual hybrid methods for the elasticity and the Stokes problems: a unified approach Numer. Math. 76 419-440
[15]  
Arnold DN(2012)A second elasticity element using the matrix bubble IMA J. Numer. Anal. 32 352-372
[16]  
Winther R(2010)A unified analysis of several mixed methods for elasticity with weak stress symmetry J. Sci. Comput. 44 156-169
[17]  
Babuška I(2014)Symmetric and conforming mixed finite elements for plane elasticity using rational bubble functions Numer. Math. 126 153-171
[18]  
Suri M(1978)Some equilibrium finite element methods for two-dimensional elasticity problems Numer. Math. 30 103-116
[19]  
Bacuta C(2013)A staggered discontinuous Galerkin method for the Stokes system SIAM J. Numer. Anal. 51 3327-3350
[20]  
Bramble JH(2006)Analysis of some low-order nonconforming mixed finite elements for linear elasticity problem Numer. Methods. Partial. Differ. Equ. 22 638-660
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