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Error analysis of the compliance model for the Signorini problem. (English) Zbl 1472.35100

Summary: The present paper is concerned with a class of penalized Signorini problems also called normal compliance models. These nonlinear models approximate the Signorini problem and are characterized both by a penalty parameter \(\varepsilon\) and by a “power parameter” \(\alpha\geq 1\), where \(\alpha=1\) corresponds to the standard penalization. We choose a continuous conforming linear finite element approximation in space dimensions \(d=2,3\) and obtain \(L^2\)-error estimates under various assumptions which are discussed and analyzed.

MSC:

35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
35J65 Nonlinear boundary value problems for linear elliptic equations
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
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