Discontinuous Galerkin methods for a contact problem with Tresca friction arising in linear elasticity

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• 作者：Kamana Porwal ^{kporwal@math.lsu.edu}
• 关键词：Finite element ; Discontinuous Galerkin ; A posteriori error estimate ; Frictional contact problem ; Variational inequalities ; Linear elasticity
• 刊名：Applied Numerical Mathematics
• 出版年：2017
• 出版时间：February 2017
• 年：2017
• 卷：112
• 期：Complete
• 页码：182-202
• 全文大小：2021 K
• 卷排序：112

文摘

In this article, we propose and analyze discontinuous Galerkin (DG) methods for a contact problem with Tresca friction for the linearized elastic material. We derive a residual based a posteriori error estimator for the proposed class of DG methods. The reliability and the efficiency of a posteriori error estimator is shown. We further investigate a priori error estimates under the minimal regularity assumption on the exact solution. An important property shared by a class of DG methods, allow us to carry out the analysis in a unified framework. Numerical experiments are reported to illustrate theoretical results.