MOVING MESH FINITE ELEMENT APPROXIMATIONS FOR VARIATIONAL INEQUALITY I: STATIC OBSTACLE PROBLEM

Finite element schemes loose accuracy when approximating a class of vari-ational inequalities, elliptic obstacle problems, due to the existence of free boundaries. In this paper, moving mesh nite element method is applied to solve the elliptic obstacle problems. Computational meshes are constructed by combining harmonic mapping and sharper a posteriori error estimators which are normally used in h-version adaptive nite element approximation. Some important issues such as the selection of monitor functions and monitor smoothing are addressed. The numerical schemes are applied to a number of test problems in two dimensions. It is shown that the moving mesh nite element methods with appropriate monitor functions eliminate (to leading order) the errors arising from the free boundaries.

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