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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Abstract
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 |
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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: | 18 Jun 2020 14:35 |
URI: | http://orca.cf.ac.uk/id/eprint/129248 |
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