Obtaining higher-order Galerkin accuracy when the boundary is polygonally approximated

2020/01/09 by Todd F. Dupont, Dupont, Todd, Johnny Guzmán +3
Engineering · Physics and Astronomy · #65N30 #Advanced Numerical Methods in Computational Mathematics #FOS: Mathematics #Model Reduction and Neural Networks #Numerical Analysis (math.NA) #Numerical methods in engineering

paper · pdf · doi:10.48550/arxiv.2001.03082

openalex publication_date 2020/01/09 · openalex created_date 2020/01/23 · openalex updated_date 2026/07/28

Abstract

We study two techniques for correcting the geometrical error associated with domain approximation by a polygon. The first was introduced some time ago \citebramble1972projection and leads to a nonsymmetric formulation for Poisson's equation. We introduce a new technique that yields a symmetric formulation and has similar performance. We compare both methods on a simple test problem.

Citations

• The Mathematical Theory of Finite Element Methods

Related

• Geometric Transformation of Finite Element Methods: Theory and Applications
• Discretization of the Poisson equation with non-smooth data and emphasis on non-convex domains
• A new anisotropic finite element method on polyhedral domains: interpolation error analysis
• An interpolated Galerkin finite element method for the Poisson equation
• A fourth-order accurate compact difference scheme for solving the\n three-dimensional Poisson equation with arbitrary boundaries