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.
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© 2008 Springer Science+Business Media, LLC
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(2008). n-Dimensional Variational Problems. In: The Mathematical Theory of Finite Element Methods. Texts in Applied Mathematics, vol 15. Springer, New York, NY. https://doi.org/10.1007/978-0-387-75934-0_6
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DOI: https://doi.org/10.1007/978-0-387-75934-0_6
Publisher Name: Springer, New York, NY
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