Error estimates for an LDG method applied to Signorini type problems. (English) Zbl 1311.74110

Summary: We propose and analyze a Local Discontinuous Galerkin method for an elliptic variational inequality of the first kind that corresponds to a Poisson equation with Signorini type condition on part of the boundary. The method uses piecewise polynomials of degree one for the field variable and of degree zero or one for the approximation of its gradient. We show optimal convergence for the method and illustrate it with some numerical experiments.


74S05 Finite element methods applied to problems in solid mechanics
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
35K85 Unilateral problems for linear parabolic equations and variational inequalities with linear parabolic operators
65K15 Numerical methods for variational inequalities and related problems
74M10 Friction in solid mechanics
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