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Recovered finite element methods on polygonal and polyhedral meshes

Dong, Zhaonan, Georgoulis, Emmanuil H. and Pryer, Tristan 2020. Recovered finite element methods on polygonal and polyhedral meshes. ESAIM: Mathematical Modelling and Numerical Analysis 54 (4) , pp. 1309-1337.

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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.

Item Type: Article
Date Type: Published Online
Status: Published
Schools: Mathematics
Publisher: EDP Sciences
ISSN: 0764-583X
Date of First Compliant Deposit: 31 January 2020
Date of Acceptance: 27 June 2019
Last Modified: 13 Mar 2021 02:26

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