Title: A Posteriori Error Control of FEM for the Elliptic Obstacle Problem.
Abstract: Elliptic obstacle problem which occurs in contact mechanics is a prototype model for a class of variational inequalities of the first kind. The linear finite element method for the obstacle performs optimally with respect to the uniform mesh refinement when the solution has full regularity. Adaptive finite element methods are useful to improve the accuracy of the numerical solution efficiently when the solution does not have full regularity. Reliable and efficient a posteriori error estimators provide us with the numerical error distribution across the computational domain and thereby plays a key role in adaptive mesh refinement procedure. In this talk, we discuss on reliable and efficient residual based a posteriori error estimates for linear finite element method for the elliptic obstacle problem. Some numerical results will be provided to illustrate the theoretical results.
