Recovered finite element methods on polygonal and polyhedral meshes

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 p...

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Bibliographic Details
Published inESAIM. Mathematical modelling and numerical analysis Vol. 54; no. 4; pp. 1309 - 1337
Main Authors Dong, Zhaonan, Georgoulis, Emmanuil H., Pryer, Tristan
Format Journal Article
LanguageEnglish
Published Les Ulis EDP Sciences 01.07.2020
Subjects
Boundary value problems
Finite element method
Galerkin method
Mathematical analysis
Polygons
Polynomials
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Summary: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.
ISSN:0764-583X
1290-3841
DOI:10.1051/m2an/2019047