Pointwise a posteriori error analysis of quadratic finite element method for the elliptic obstacle problem

Abstract

In this article, we study a posteriori error analysis of quadratic finite element method in the maximum norm for the elliptic obstacle problem. We discuss the reliability and the efficiency of the proposed a posteriori error estimator. In the analysis, regularized Green’s function plays a crucial role and together with that, in obtaining the sign of the discrete Lagrange multiplier we have exploited the property that midpoint quadrature rules are exact for quadratic polynomials. Numerical results are performed to illustrate the convergence behavior of a posteriori error estimator through various test examples.