Superconvergence analysis of finite element method for a second-type variational inequality
Summary: This paper studies the finite element (FE) approximation to a second-type variational inequality. The superclose and superconvergence results are obtained for conforming bilinear FE and nonconforming EQ\(^{\text{rot}}\) FE schemes under a reasonable regularity of the exact solution \(u \in H^{5/2}(\Omega)\), which seem to be never discovered in the previous literature. The optimal \(L^2\)-norm error estimate is also derived for EQ\(^{\text{rot}}\) FE. At last, some numerical results are provided to verify the theoretical analysis.
scientific article; zbMATH DE number 6169848
scientific article