An optimal adaptive mixed finite element method

Carstensen, Carsten; Rabus, Hella

doi:10.1090/S0025-5718-2010-02397-X

An optimal adaptive mixed finite element method
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by Carsten Carstensen and Hella Rabus PDF

Math. Comp. 80 (2011), 649-667

Abstract:

Various applications in fluid dynamics and computational continuum mechanics motivate the development of reliable and efficient adaptive algorithms for mixed finite element methods. In order to save degrees of freedom, not all but just a selection of finite element domains are refined. Hence the fundamental question of convergence as well as the question of optimality require new mathematical arguments. The presented adaptive algorithm for Raviart-Thomas mixed finite element methods solves the Poisson model problem, with optimal convergence rate.

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