Recovered finite element methods on polygonal and polyhedral meshes

Dong, Zhaonan; Georgoulis, Emmanuil H.; Pryer, Tristan

doi:10.1051/m2an/2019047

Dong, Zhaonan ; Georgoulis, Emmanuil H. ; Pryer, Tristan

ESAIM: Mathematical Modelling and Numerical Analysis , Tome 54 (2020) no. 4, pp. 1309-1337.

Suite au passage du modèle économique de la revue en S20, le texte intégral des articles des années 2019 et 2020 est accessible uniquement sur le site de l'éditeur et est réservé aux abonnés.

Résumé

Recovered Finite Element Methods (R-FEM) have been recently introduced in Georgoulis and Pryer [Comput. Methods Appl. Mech. Eng. 332 (2018) 303–324]. for meshes consisting of simplicial and/or box-type elements. Here, utilising the flexibility of the R-FEM framework, we extend their definition to polygonal and polyhedral meshes in two and three spatial dimensions, respectively. An attractive feature of this framework is its ability to produce arbitrary order polynomial conforming discretizations, yet involving only as many degrees of freedom as discontinuous Galerkin methods over general polygonal/polyhedral meshes with potentially many faces per element. A priori error bounds are shown for general linear, possibly degenerate, second order advection-diffusion-reaction boundary value problems. A series of numerical experiments highlight the good practical performance of the proposed numerical framework.

MR Zbl

DOI : 10.1051/m2an/2019047

Classification : 65N30, 65N50, 65N55
Mots-clés : Recovered finite element method, polygonal and polyhedral meshes, $$ analysis, PDEs with non-negative characteristic form

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     title = {Recovered finite element methods on polygonal and polyhedral meshes},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
     pages = {1309--1337},
     publisher = {EDP-Sciences},
     volume = {54},
     number = {4},
     year = {2020},
     doi = {10.1051/m2an/2019047},
     mrnumber = {4113053},
     zbl = {1446.65165},
     language = {en},
     url = {http://www.numdam.org/articles/10.1051/m2an/2019047/}
}

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Dong, Zhaonan; Georgoulis, Emmanuil H.; Pryer, Tristan. Recovered finite element methods on polygonal and polyhedral meshes. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 54 (2020) no. 4, pp. 1309-1337. doi : 10.1051/m2an/2019047. http://www.numdam.org/articles/10.1051/m2an/2019047/

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