Stability and Convergence of Higher Order Finite Element Methods for Partial Differential Equations

Dr. Tadeusz Janik

Department of Mathematical Sciences
University of Alabama in Huntsville

October 24, 1997

Abstract

Higher-order methods for solving some classes of diffusion, elasticity, and fluid-flow problems lead to interesting questions on stability and approximability. It is possible for some of these problems to achieve high accuracy by using a finite element approach with higher-order piecewise-polynomials on a subdivision of the domain. These methods are usually called p- or hp-versions of the finite element methods of Galerkin spectral element methods.

In view of the lack of stability for some choice of discrete spaces, we are interested in the question whether it is possible to define stable discrete spaces with quasi-optimal approximation properties.