The TRUNC element in any dimension and application to a modified Poisson equation
Abstract We introduce a novel TRUNC finite element in 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.
Authors
- Hongliang Li (ORCID: https://orcid.org/0009-0000-2032-3462)
- Yinghong Zhou (ORCID: https://orcid.org/0009-0006-0692-2606)
- Pingbing Ming (ORCID: https://orcid.org/0000-0002-0779-1576)
Institutions
- Chinese Academy of Sciences (CN)
- Academy of Mathematics and Systems Science (CN)
- University of Chinese Academy of Sciences (CN)
- Sichuan Normal University (CN)
Publication Details
- Journal
- Numerical Methods for Partial Differential Equations
- Published
- 2024-10-02
- DOI
- https://doi.org/10.1002/num.23151
- Primary Topic
- Advanced Numerical Methods in Computational Mathematics
- Type
- article
- Field-Weighted Citation Impact
- 0.00
Funders
- National Natural Science Foundation of China
- Sichuan Province Science and Technology Support Program