Displaying similar documents to “Local accuracy in finite element analysis using curved isoparametric elements”

Finite element methods on non-conforming grids by penalizing the matching constraint

Eric Boillat (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

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The present paper deals with a finite element approximation of partial differential equations when the domain is decomposed into sub-domains which are meshed independently. The method we obtain is never conforming because the continuity constraints on the boundary of the sub-domains are not imposed strongly but only penalized. We derive a selection rule for the penalty parameter which ensures a quasi-optimal convergence.

Greedy Algorithms for Adaptive Approximation

Albert Cohen (2009)

Bollettino dell'Unione Matematica Italiana

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We discuss the performances of greedy algorithms for two problems of numerical approximation. The first one is the best approximation of an arbitrary function by an N-terms linear combination of simple functions adaptively picked within a large dictionary. The second one is the approximation of an arbitrary function by a piecewise polynomial function on an optimally adapted triangulation of cardinality N. Performance is measured in terms of convergence rate with respect to the number...

Generalizations of the Finite Element Method

Marc Schweitzer (2012)

Open Mathematics

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This paper is concerned with the generalization of the finite element method via the use of non-polynomial enrichment functions. Several methods employ this general approach, e.g. the extended finite element method and the generalized finite element method. We review these approaches and interpret them in the more general framework of the partition of unity method. Here we focus on fundamental construction principles, approximation properties and stability of the respective numerical...

A unified analysis of elliptic problems with various boundary conditions and their approximation

Jérôme Droniou, Robert Eymard, Thierry Gallouët, Raphaèle Herbin (2020)

Czechoslovak Mathematical Journal

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We design an abstract setting for the approximation in Banach spaces of operators acting in duality. A typical example are the gradient and divergence operators in Lebesgue-Sobolev spaces on a bounded domain. We apply this abstract setting to the numerical approximation of Leray-Lions type problems, which include in particular linear diffusion. The main interest of the abstract setting is to provide a unified convergence analysis that simultaneously covers (i) all usual boundary conditions,...