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

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:254

Article

Gwinner, Joachim

关键词: hp-version of the finite element method;    Cea-Falk error estimate;    Gauss-Lobatto quadrature;    Nonsmooth boundary value problem;    Unilateral contact;    Semicoercive variational inequality;   

DOI  :  10.1016/j.cam.2013.03.013

来源: Elsevier

【 摘 要 】

This paper is concerned with the convergence of the hp-version of the finite element method (hp-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 hp-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 Cea-Falk estimate and operator interpolation arguments, we establish an a priori error estimate in the energy norm under a reasonable regularity assumption. (C) 2013 Elsevier B.V. All rights reserved.

【 授权许可】

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