Published In
Computers & Mathematics with Applications
Document Type
Pre-Print
Publication Date
2-2022
Subjects
Boundary element methods, Polygons, Polyhedra
Abstract
Abstract
H1" role="presentation" style="box-sizing: border-box; margin: 0px; padding: 0px; display: inline-block; line-height: normal; font-size: 16.2px; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; position: relative;">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.
Locate the Document
DOI
10.1016/j.camwa.2021.12.003
Persistent Identifier
https://archives.pdx.edu/ds/psu/37923
Citation Details
Ovall, J. S., & Reynolds, S. E. (2022). Quadrature for implicitly-defined finite element functions on curvilinear polygons. Computers & Mathematics with Applications, 107, 1-16.
Description
This is the author’s version of a work. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document.