Convergence of a stabilized discontinuous Galerkin method for incompressible nonlinear elasticity

被引：15

作者：

Baroli, Davide ^{[1
]}

Quarteroni, Alfio ^{[2
,3
]}

Ruiz-Baier, Ricardo ^{[2
]}

机构：

[1] Univ Insubria, Dipartimento Fis & Matemat, I-22100 Como, Italy

[2] Ecole Polytech Fed Lausanne, CMCS MATHICSE SB, CH-1015 Lausanne, Switzerland

[3] Politecn Milan, Dipartimento Matemat, MOX Modellist & Calcolo Sci, I-20133 Milan, Italy

来源：

ADVANCES IN COMPUTATIONAL MATHEMATICS | 2013年 / 39卷 / 02期

基金：

欧洲研究理事会;

关键词：

Nonlinear elasticity; Discontinuous Galerkin formulation; Incompressible material; Edge-based stabilization; FINITE-ELEMENT-METHOD; APPROXIMATION;

D O I：

10.1007/s10444-012-9286-8

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper we present a discontinuous Galerkin method applied to incompressible nonlinear elastostatics in a total Lagrangian deformation-pressure formulation, for which a suitable interior penalty stabilization is applied. We prove that the proposed discrete formulation for the linearized problem is well-posed, asymptotically consistent and that it converges to the corresponding weak solution. The derived convergence rates are optimal and further confirmed by a set of numerical examples in two and three spatial dimensions.

引用

页码：425 / 443

页数：19

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