A Local Regularization Operator for Triangular and Quadrilateral Finite Elements
SIAM Journal on Numerical Analysis
Positivity preserving finite element approximation
Mathematics of Computation
Mixed finite element methods for unilateral problems: convergence analysis and numerical studies
Mathematics of Computation
Hybrid finite element methods for the Signorini problem
Mathematics of Computation
Monotone Multigrid Methods on Nonmatching Grids for Nonlinear Multibody Contact Problems
SIAM Journal on Scientific Computing
An Optimal A Priori Error Estimate for Nonlinear Multibody Contact Problems
SIAM Journal on Numerical Analysis
Mixed Finite Element Methods for Smooth Domain Formulation of Crack Problems
SIAM Journal on Numerical Analysis
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This paper is concerned with the frictionless unilateral contact problem (i.e., a Signorini problem with the elasticity operator). We consider a mixed finite element method in which the unknowns are the displacement field and the contact pressure. The particularity of the method is that it furnishes a normal displacement field and a contact pressure satisfying the sign conditions of the continuous problem. The a priori error analysis of the method is closely linked with the study of a specific positivity preserving operator of averaging type which differs from the one of Chen and Nochetto. We show that this method is convergent and satisfies the same a priori error estimates as the standard approach in which the approximated contact pressure satisfies only a weak sign condition. Finally we perform some computations to illustrate and compare the sign preserving method with the standard approach.