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 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.

Original languageEnglish
Pages (from-to)1309-1337
Number of pages29
JournalESAIM: Mathematical Modelling and Numerical Analysis
Volume54
Issue number4
Early online date18 Jun 2020
DOIs
Publication statusPublished - 1 Jul 2020

Keywords

  • A priori analysis
  • PDEs with non-negative characteristic form
  • Polygonal and polyhedral meshes
  • Recovered finite element method

ASJC Scopus subject areas

  • Analysis
  • Numerical Analysis
  • Modelling and Simulation
  • Computational Mathematics
  • Applied Mathematics

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