Galerkin finite element methods for parabolic problems / Vidar Thomée

From the preface: "The purpose of this work is to present, in an essentially self-contained form, a survey of the mathematics of Galerkin finite element methods as applied to parabolic problems. The selection of topics is not meant to be exhaustive, but rather reflects the author's involvement in the field over the past ten years. The goal has been mainly pedagogical, with emphasis on collecting ideas and methods of analysis in simple model situations, rather than on pursuing each approach to its limits. The notes thus summarize recent developments, and the reader is often referred to the literature for more complete results on a given topic. Because the formulation and analysis of Galerkin methods for parabolic problems are generally based on facts concerning the corresponding stationary elliptic problems, the necessary elliptic results are included in the text for completeness."