Recovery-based error estimators for the VEM and BEM-based FEM

Seibel, Daniel; Weißer, Steffen

doi:10.1016/j.camwa.2020.09.004

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“…[1, 4-6, 9-16, 20]), Boundary Element-Based Finite Element Methods (BEM-FEM) (cf. [26,[32][33][34][39][40][41][42][43][44]) and Trefftz-type Finite Element Methods (Trefftz-FEM) (cf. [2,3,18,24,25]) all employ vector spaces that are implicitly defined, as in (1).…”

Section: Introductionmentioning

confidence: 99%

Quadrature for Implicitly-defined Finite Element Functions on Curvilinear Polygons

Ovall¹,

Reynolds²

2021

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H 1 -conforming Galerkin methods on polygonal meshes such as VEM, BEM-FEM and Trefftz-FEM employ local finite element functions that are implicitly defined as solutions of Poisson problems having polynomial source and boundary data. Recently, such methods have been extended to allow for mesh cells that are curvilinear polygons. Such extensions present new challenges for determining suitable quadratures. We describe an approach for integrating products of these implicitly defined functions, as well as products of their gradients, that reduces integrals on cells to integrals along their boundaries. Numerical experiments illustrate the practical performance of the proposed methods.

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