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Erschienen in:
2021 | OriginalPaper | Buchkapitel
2. Weak derivatives and Sobolev spaces
verfasst von : Alexandre Ern, Jean-Luc Guermond
Erschienen in: Finite Elements I
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Abstract
We investigate the notion of differentiation for Lebesgue integrable functions. We introduce an extension of the classical concept of derivative and partial derivative which is called weak derivative. This notion is used throughout the book. We also introduce the concept of Sobolev spaces. These spaces are useful to study the well-posedness of partial differential equations and their approximation using finite elements.