Conforming virtual element method for nondivergence form linear elliptic equations with Cordes coefficients
We propose and analyze an [Formula: see text]-conforming virtual element method (VEM) for the simplest linear elliptic PDEs in nondivergence form with Cordes coefficients. The VEM hinges on a hierarchical construction valid for any dimension [Formula: see text]. The analysis relies on the continuous Miranda–Talenti estimate for convex domains [Formula: see text] and is rather elementary. We prove stability and error estimates in [Formula: see text], including the effect of quadrature, under minimal regularity of the data. Numerical experiments illustrate the interplay of coefficient regularity and convergence rates in [Formula: see text].
Authors
- Ricardo H. Nochetto (ORCID: https://orcid.org/0009-0002-8895-1144)
- Andrea Cangiani (ORCID: https://orcid.org/0000-0002-5489-2425)
- Guillaume Bonnet (ORCID: https://orcid.org/0000-0001-8635-1175)
Institutions
- Centre National de la Recherche Scientifique (FR)
- Scuola Internazionale Superiore di Studi Avanzati (IT)
- Centre de Recherche en Mathématiques de la Décision (FR)
- Université Paris Sciences et Lettres (FR)
- Université Paris Dauphine-PSL (FR)
- University of Maryland, College Park (US)
Publication Details
- Journal
- Mathematical Models and Methods in Applied Sciences
- Published
- 2024-11-29
- DOI
- https://doi.org/10.1142/s0218202525500034
- Citations
- 1
- Primary Topic
- Advanced Numerical Methods in Computational Mathematics
- Type
- article
- Field-Weighted Citation Impact
- 0.37
Funders
- National Natural Science Foundation of China
- European Social Fund