Grading Functions and Mesh Redistribution

Abstract

We consider the problem of determining an appropriate grading of a mesh for piecewise polynomial interpolation and for approximate solution of two-point boundary-value problems by finite difference or finite element methods. An analysis of optimality of the mesh and optimal grading functions in various norms and seminorms for the interpolation problem leads to the formulation of an adaptive mesh redistribution algorithm for boundary-value problems in one dimension. Error estimates are given and numerical results presented to demonstrate the performance of the scheme and compare alternative redistribution criteria.