Some general lagrange interpolations over simplex finite elements with reference to derivative singularities

Abstract

For simplex finite elements, the native Lagrange family with arbitrarily placed nodes is presented in hierarchy-ranking expressions. It includes the well-known complete Lagrange family as well as the mid-edge Lagrange family to be proposed in this paper. This new family enables us to utilize harmonious combinations of interpolations of different orders in finite element analysis. As an application of developed simplex interpolations to fracture mechanics where some derivative singularities are needed, we then describe the semi-radial singularity mapping with examinations of peculiar trial function spaces.