A Local Regularization Operator for Triangular and Quadrilateral Finite Elements

TL;DR: A local regularization operator on triangular or quadrilateral finite elements built on structured or unstructured meshes is developed and it is proved that it has the same optimal approximation properties as the standard interpolation operator.

Abstract: 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 Clement; 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.