A NITSCHE-BASED METHOD FOR UNILATERAL CONTACT PROBLEMS: NUMERICAL ANALYSIS

被引：87

作者：

Chouly, Franz ^{[1
]}

Hild, Patrick ^{[2
]}

机构：

[1] Univ Franche Comte, UMR CNRS 6623, Math Lab, F-25030 Besancon, France

[2] Univ Toulouse 3, UMR CNRS 5219, Inst Math Toulouse, F-31062 Toulouse 9, France

来源：

SIAM JOURNAL ON NUMERICAL ANALYSIS | 2013年 / 51卷 / 02期

关键词：

unilateral contact; finite elements; Nitsche's method; FINITE-ELEMENT METHODS; PRIORI ERROR ESTIMATE; SIGNORINI PROBLEM; VARIATIONAL-INEQUALITIES; BOUNDARY-CONDITIONS; LINEAR ELASTICITY; SOLID MECHANICS; APPROXIMATIONS; CONVERGENCE; SIMULATION;

D O I：

10.1137/12088344X

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We introduce a Nitsche-based finite element discretization of the unilateral contact problem in linear elasticity. It features a weak treatment of the nonlinear contact conditions through a consistent penalty term. Without any additional assumption on the contact set, we can prove theoretically its fully optimal convergence rate in the H-1(Omega)-norm for linear finite elements in two dimensions, which is O(h(1/2 + nu)) when the solution lies in H3/2 + nu(Omega), 0 < nu <= 1/2. An interest of the formulation is that, as opposed to Lagrange multiplier-based methods, no other unknown is introduced and no discrete inf-sup condition needs to be satisfied.

引用

页码：1295 / 1307

页数：13

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