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 FE schemes under a reasonable regularity of the exact solution , which seem to be never discovered in the previous literature. The optimal -norm error estimate is also derived for FE. At last, some numerical results are provided to verify the theoretical analysis.
Dongyang Shi. Hongbo Guan. Xiaofei Guan. "Superconvergence Analysis of Finite Element Method for a Second-Type Variational Inequality." J. Appl. Math. 2012 1 - 12, 2012. https://doi.org/10.1155/2012/156095