Special Finite Element Methods for a Class of Second Order Elliptic Problems wth Rough Coefficients.

摘要

In this paper we consider the approximate solution of a class of second order elliptic equations with rough coefficients. Problem of the type considered arise in the analysis of unidirectional composites, where the coefficients represent the properties of the material. We present several methods for this class of problem, and show that they have the same accuracy as usual methods have for problem with smooth coefficients. We refer to the methods as special finite elements methods because they are of finite element type but employ special shape functions, chosen to effectively model the unknown solution.