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Erschienen in:
2008 | OriginalPaper | Buchkapitel
n-Dimensional Variational Problems
Erschienen in: The Mathematical Theory of Finite Element Methods
Verlag: Springer New York
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We now give several examples of higher-dimensional variational problems that use the theory developed in previous chapters. The basic notation is provided by the Sobolev spaces developed in Chapter 1. We combine the existence theory of Chapter 2 together with the approximation theory of Chapters 3 and 4 to provide a complete theory for the discretization process. Several examples will be fully developed in the text, and several others are found in the exercises. Throughout this chapter, we assume that the domain Ω is bounded.