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Erschienen in:
2009 | OriginalPaper | Buchkapitel
Lectures on Adaptive Mixed Finite Element Methods
verfasst von : C. Carstensen
Erschienen in: Mixed Finite Element Technologies
Verlag: Springer Vienna
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These lectures concern the three most simple model problems of elliptic second order partial differential equations which allow for some mixed formulations. The introduction to the Poisson problem, to the Stokes problem, and to linear elasticity is completely standard and hence kept rather short.
The first aim is a general discussion of the mixed formulations around various statements of the inf-sup condition often named after Ladyzhenskaya, Babuška, Brezzi. Some details on the implementation of Raviart-Thomas mixed finite elements in MATLAB complement this introduction.
The second aim is a particular outline of the author’s own research on a posteriori error analysis and adaptive algorithms of mixed finite element methods displayed for the Poisson problem. The presentation is motivated by the author’s research (
2004
); (
1997
),
1999
,(
2005
); (
1998
); (
2000
); (
2001a
),(
b
); (
1999
) with essential help of many researchers including S. Bartels, D. Braess, G. Dolzmann, S.A. Funken and R. Hoppe.