Circumventing Babuska's Paradox Using Hexspherical Finite Elements
by
A. J. Meir
Department of Mathematics, Auburn University
Coauthors: P. G. Schmidt

The so-called Babuska's paradox is a well-known affliction affecting the accuracy of finite-element approximations of solutions of fourth-order elliptic partial differential equations (and of certain second-order systems of such equations) posed on domains with curved boundaries. When considering second-order problems on domains with spherical (circular) symmetry, the paradox can be easily overcome by using ``hexspherical'' finite elements, even when using low-order elements and standard weak forms. In essence, the idea is to map a given physical domain with spherical symmetry to a computational domain with hexahedral symmetry, thereby avoiding polygonal approximations of the curved boundary of the physical domain. We will describe ``hexspherical'' finite elements and discuss some computer experiments for a model problem.

A. J. Meir

Date received: March 31, 1999