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Erschienen in:
2021 | OriginalPaper | Buchkapitel
4. Error analysis with variational crimes
verfasst von : Alexandre Ern, Jean-Luc Guermond
Erschienen in: Finite Elements II
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Abstract
This chapter departs from the ideal setting analyzed in the previous chapter. The approximation is no longer conforming, and the consequences of various so-called variational crimes are studied. The main results of this chapter are upper bounds on the approximation error in terms of the best-approximation error of the exact solution by members of the discrete trial space. These error estimates are based on the notions of stability and consistency/boundedness. Combined with an approximability property, they prove that the approximation method is convergent. Two simple examples illustrate the theory: a first-order PDE approximated by the Galerkin/least-squares technique and a second-order PDE approximated by a boundary penalty method.