An Analysis of the Finite Element Method for Second Order Elliptic Boundary Value Problems. An Introduction

Abstract

These notes represent an expansion of lectures given at Dusseldorf in the summer of 1987. It is hoped that they will provide an introduction to the mathematical analysis of the finite element method for second order elliptic boundary value problems. They are geared towards students who have a good background in analysis but are not familiar with the finite element method. Thus we start at the beginning with the aim of understanding the method and developing basic techniques and ideas which seem to be fundamental to it. The treatment here is neither exhaustive nor general. Rather, topics are covered which we feel address important problems whose solutions make use of basic techniques. We have attempted to give selfcontained proofs wherever possible. It is hoped that these will be adequate in order that the student be able to understand some recent results in the field. For the convenience of the student a bibliography has been included which covers some topics not treated in these notes.