ABSTRACT

Chapter 1

Introduction

As stated in the preface, we assume that the reader knows the basic concepts

of the nite element method (see, e.g., [11, 39, 46, 47, 119, 178, 180, 191]).

Nevertheless, let us review at least the most commonly used concepts { scalar

and vector-valued Hilbert spaces, trivia of nite elements in these spaces,

basic principles of the discretization of time-independent and evolutionary

problems and a few additional topics that will be important for higher-order

nite element technology.