An analysis of finite volume element method for solving the Signorini problem

We propose and analyze the finite volume element method for solving the Signorini problem. The stability and the optimal H1-convergence rate are given. Particularly, we establish a superclose interpolation estimate for the bilinear form of this method. Based on this estimate and the interpolation post-processing technique, we derive an O(h32)-order superconvergence in the H1-norm under a proper regularity condition. Finally, an asymptotically exact a posteriori error estimator also is given for the error ∥u−uh∥1∥u−uh∥1.