Constraints Coefficients in hp-FEM

Abstract

Continuity requirements on irregular meshes enforce a proper constraint of the degrees of freedom that correspond to hanging nodes, edges or faces. This is achieved by using so-called constraints coefficients which are obtained from the appropriate coupling of shape functions.

In this note, a general framework for determining the constraints coefficients of tensor product shape functions is presented and its application to shape functions using integrated Legendre or Gauss-Lobatto polynomials. The constraints coefficients in the one-dimensional case are determined via recurrence relations. The constraints coefficients in the multi-dimensional case are obtained as products of these coefficients. The coefficients are available for arbitrary patterns of subdivisions.