2021/06/01 by Jeffrey S. Ovall, Ovall, Jeffrey, Samuel Reynolds +1
Engineering · #31A30 #65D30 #65D32 #65N30 #65R20 #Advanced Numerical Methods in Computational Mathematics #Elasticity and Material Modeling #FOS: Mathematics #Numerical Analysis (math.NA) #Numerical methods in engineering
paper · pdf · doi:10.48550/arxiv.2106.00796
openalex publication_date 2021/06/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.