Quadrature for implicitly-defined finite element functions on curvilinear polygons

H1-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 tha...

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Bibliographic Details
Published inComputers & mathematics with applications (1987) Vol. 107; pp. 1 - 16
Main Authors Ovall, Jeffrey S., Reynolds, Samuel E.
Format Journal Article
LanguageEnglish
Published Oxford Elsevier Ltd 01.02.2022
Elsevier BV
Subjects
Curvilinear polygon
Finite element method
Galerkin method
Integrals
Polygons
Polynomials
Quadrature
Trefftz-FEM
VEM
Quadrature
Curvilinear polygon
Trefftz-FEM
VEM
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ISSN0898-1221
1873-7668
DOI10.1016/j.camwa.2021.12.003

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Summary:H1-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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ISSN:0898-1221
1873-7668
DOI:10.1016/j.camwa.2021.12.003