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

Abstract

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 ${\text{EQ}}^{\text{rot}}$ FE schemes under a reasonable regularity of the exact solution $u\in H^{5/2}(\mathrm{\Omega })$, which seem to be never discovered in the previous literature. The optimal $L^2$-norm error estimate is also derived for ${\text{EQ}}^{\text{rot}}$ FE. At last, some numerical results are provided to verify the theoretical analysis.