A Local Regularization Operator for Triangular and Quadrilateral Finite Elements

This paper develops a local regularization operator on triangular or quadrilateral finite elements built on structured or unstructured meshes. This operator is a variant of the regularization operator of Clément; however, ours is constructed via a local projection in a reference domain. We prove in this paper that it has the same optimal approximation properties as the standard interpolation operator, and we present some applications.