Optimal convergence analysis of the unilateral contact problem with and without Tresca friction conditions by the penalty method

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:472

Article

Dione, Ibrahima¹ 

[1] Univ Laval, Dept Math & Stat, Pavillon Vachon,1045 Ave Med, Quebec City, PQ G1V 0A6, Canada

关键词: A priori estimate;    Finite elements;    Linear elasticity;    Penalty method;    Unilateral contact;    Tresca friction;   

DOI  :  10.1016/j.jmaa.2018.11.023

来源: Elsevier

【 摘 要 】

We study the linear finite element approximation of the elasticity equations with and without unilateral friction contact (of Tresca type) conditions in a polygonal or polyhedral domain. The unilateral contact condition is weakly imposed by the penalty method. We derive error estimates which depend on the penalty parameter epsilon and the mesh size h. In fact, under the H3/2+nu (Omega), 0 < v <= 1/2, regularity of the solution of the contact problems (with and without friction) and with the requirement epsilon > h, we prove a convergence rate of O (h(1/2+nu) + epsilon(1/2+nu)) in the energy norm. Therefore, if the penalty parameter is taken as epsilon := ch(theta) where 0 < theta <= 1, the convergence rate of O (h(theta(1/2+nu))) is obtained. In particular, we obtain an optimal linear convergence when e behaves like h (i.e. theta = 1) and nu = 1/2. (C) 2018 Elsevier Inc. All rights reserved.

【 授权许可】

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