An optimal adaptive mixed finite element method

Please always quote using this URN:urn:nbn:de:0296-matheon-5757
  • 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 some selected set 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. Chen, Holst, and Xu presented "convergence and optimality of adaptive mixed finite element methods" (2008) following arguments of Rob Stevenson for the conforming finite element method. Their algorithm reduces oscillations separately, before approximating the solution by some adaptive algorithm in the spirit of W. Dörfler (1996). The algorithm proposed here appears more natural in switching to either reduction of the edge-error estimator or of the oscillations.

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Metadaten
Author:Carsten Carstensen, Hella Rabus
URN:urn:nbn:de:0296-matheon-5757
Referee:Harry Yserentant
Document Type:Preprint, Research Center Matheon
Language:English
Date of first Publication:2009/05/03
Release Date:2009/02/26
Tag:
Institute:Humboldt-Universität zu Berlin
MSC-Classification:65-XX NUMERICAL ANALYSIS / 65Nxx Partial differential equations, boundary value problems / 65N12 Stability and convergence of numerical methods
65-XX NUMERICAL ANALYSIS / 65Nxx Partial differential equations, boundary value problems / 65N15 Error bounds
65-XX NUMERICAL ANALYSIS / 65Nxx Partial differential equations, boundary value problems / 65N30 Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods
65-XX NUMERICAL ANALYSIS / 65Nxx Partial differential equations, boundary value problems / 65N50 Mesh generation and refinement
65-XX NUMERICAL ANALYSIS / 65Yxx Computer aspects of numerical algorithms / 65Y20 Complexity and performance of numerical algorithms [See also 68Q25]
Preprint Number:569
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