Superconvergence Analysis of Finite Element Method for a Second-Type Variational Inequality

This paper studies the finite element (FE) approximation to a second-type variational inequality. The supe rclose and superconvergence results are obtained for conforming bilinear FE and nonconforming EQrot FE schemes under a reasonable regularity of the exact solution u∈H5/2(Ω), which seem to be never discovered in the previous literature. The optimal L2-norm error estimate is also derived for EQrot FE. At last, some numerical results are provided to verify the theoretical analysis

An error estimate for the Signorini problem with Coulomb friction approximated by finite elements

International audienceThe present paper is concerned with the unilateral contact model and the Coulomb friction law in linear elastostatics. We consider a mixed formulation in which the unknowns are the displacement field and the normal and tangential constraints on the contact area. The chosen finite element method involves continuous elements of degree one and continuous piecewise affine multipliers on the contact zone. A convenient discrete contact and friction condition is introduced in order to perform a convergence study. We finally obtain a first a priori error estimate under the assumptions ensuring the uniqueness of the solution to the continuous problem