A residual based a posteriori error estimator is derived for
a quadratic finite element method (FEM) for the elliptic obstacle
problem. The error estimator involves various residuals consisting
of the data of the problem, discrete solution and a Lagrange
multiplier related to the obstacle constraint. The choice of the
discrete Lagrange multiplier yields an error estimator that is
comparable with the error estimator in the case of linear FEM.
Further, an a priori error estimate is derived to show that
the discrete Lagrange multiplier converges at the same rate as
that of the discrete solution of the obstacle problem. The
numerical experiments of adaptive FEM show optimal order
convergence. This demonstrates that the quadratic FEM for obstacle
problem exhibits optimal performance.
CMAM considers original mathematical contributions to computational methods and numerical analysis with applications mainly related to PDEs. The journal is interdisciplinary while retaining the common thread of numerical analysis, readily readable and meant for a wide circle of researchers in applied mathematics.