Recovered finite element methods on polygonal and polyhedral meshes

Zhaonan Dong, Emmanuil H. Georgoulis, Tristan Pryer

Research output: Contribution to journalArticle

Abstract

Recovered finite element methods (R-FEM) have been recently introduced for meshes consisting of simplicial and/or box-type meshes. Here, utilising the flexibility of R-FEM framework, we extend their definition on polygonal and polyhedral meshes in two and three spatial dimensions, respectively. A key attractive feature of this framework is its ability to produce 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 highlights the good practical performance of the proposed numerical framework.
Original languageEnglish
JournalESAIM: Mathematical Modelling and Numerical Analysis
Publication statusAccepted/In press - 27 Jun 2019

Keywords

  • math.NA

Cite this

Recovered finite element methods on polygonal and polyhedral meshes. / Dong, Zhaonan; Georgoulis, Emmanuil H.; Pryer, Tristan.

In: ESAIM: Mathematical Modelling and Numerical Analysis, 27.06.2019.

Research output: Contribution to journalArticle

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