These are the lecture notes of the seminar "Mathematische Theorie der
finiten Element- und Randelementmethoden" organized by the "Deutsche
Mathematiker-Vereinigung" and held in Dusseldorf from 07. - 14. of June
1987. Finite element methods and the closely related boundary element
methods nowadays belong to the standard routines for the computation of
solutions to boundary and initial boundary value problems of partial
differential equations with many applications as e.g. in elasticity and
thermoelasticity, fluid mechanics, acoustics, electromagnetics, scatter-
ing and diffusion. These methods also stimulated the development of
corresponding mathematical numerical analysis. I was very happy that A.
Schatz and V. Thomee generously joined the adventure of the seminar and
not only gave stimulating lectures but also spent so much time for
personal discussion with all the participants. The seminar as well as
these notes consist of three parts: 1. An Analysis of the Finite Element
Method for Second Order Elliptic Boundary Value Problems by A. H.
Schatz. II. On Finite Elements for Parabolic Problems by V. Thomee. III.
I30undary Element Methods for Elliptic Problems by \V. L. Wendland. The
prerequisites for reading this book are basic knowledge in partial
differential equations (including pseudo-differential operators) and in
numerical analysis. It was not our intention to present a comprehensive
account of the research in this field, but rather to give an
introduction and overview to the three different topics which shed some
light on recent research.
