The TRUNC element in any dimension and application to a modified Poisson equation
Numerical Analysis
2024-09-04 v1 Numerical Analysis
Abstract
We introduce a novel TRUNC finite element in n dimensions, encompassing the traditional TRUNC triangle as a particular instance. By establishing the weak continuity identity, we identify it as crucial for error estimate. This element is utilized to approximate a modified Poisson equation defined on a convex polytope, originating from the nonlocal electrostatics model. We have substantiated a uniform error estimate and conducted numerical tests on both the smooth solution and the solution with a sharp boundary layer, which align with the theoretical predictions.
Cite
@article{arxiv.2409.00748,
title = {The TRUNC element in any dimension and application to a modified Poisson equation},
author = {Hongliang Li and Pingbing Ming and Yinghong Zhou},
journal= {arXiv preprint arXiv:2409.00748},
year = {2024}
}