-FEM convergence for unilateral contact problems with Tresca friction in plane linear elastostatics

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• 作者：Joachim Gwinner ; ^{joachim.gwinner@unibw-muenchen.de}
• 关键词：hphp-version of the finite element method ; Cé ; a&ndash ; Falk error estimate ; Gauss&ndash ; Lobatto quadrature ; Nonsmooth boundary value problem ; Unilateral contact ; Semicoercive variational inequality
• 刊名：Journal of Computational and Applied Mathematics
• 出版年：2013
• 出版时间：15 December, 2013
• 年：2013
• 卷：254
• 期：Complete
• 页码：175-184
• 全文大小：429 K

文摘

This paper is concerned with the convergence of the -version of the finite element method (-FEM) for some nonsmooth unilateral problems in linear elastostatics. We consider in particular the deformation of an elastic body unilaterally supported by a rigid foundation, admitting Tresca friction (given friction) along the rigid foundation, solely subjected to body forces and surface tractions without being fixed along some part of its boundary. For the discretization of the unilateral constraint and the nonsmooth friction functional we employ Gauss-Lobatto quadrature. We show convergence of the -FEM approximations for mechanically definite problems without imposing any regularity assumption. Moreover we treat the coercive case, when the body is fixed along some part of the boundary. Based on an abstract C¨¦a-Falk estimate and operator interpolation arguments, we establish an a priori error estimate in the energy norm under a reasonable regularity assumption.