Quasi-regional mapping for the p-version of the finite element method

Abstract

In the p-version of the finite element method the size of the elements is fixed independently of the number of degrees of freedom. Therefore, accurate representation of the curves and surfaces which bound the solution domain, so that the quality of the representation is independent of the number of elements, is very important. Another important requirement is that continuous curves and surfaces must be represented either directly, such as in the blending function method, or must be approximated with sufficient accuracy for the discretization error to be controlled by the mesh and the polynomial degree of elements, rather than the mapping of the elements. In this paper we describe a unified representation scheme in which all boundary curves and surfaces are approximated by piecewise polynomials. Special selection of the collocation points provides approximate continuity between elements on smooth boundary curves and surfaces. A numerical example is also presented.