Arbitrary-order intrinsic virtual element method for elliptic equations on surfaces.
Geometrically intrinsic operators
Polygonal mesh
Surface PDEs
Virtual element method
high-order methods
Journal
Calcolo
ISSN: 1126-5434
Titre abrégé: Calcolo
Pays: Italy
ID NLM: 9918284265606676
Informations de publication
Date de publication:
2021
2021
Historique:
received:
16
12
2020
revised:
03
05
2021
accepted:
15
05
2021
entrez:
22
11
2021
pubmed:
23
11
2021
medline:
23
11
2021
Statut:
ppublish
Résumé
We develop a geometrically intrinsic formulation of the arbitrary-order Virtual Element Method (VEM) on polygonal cells for the numerical solution of elliptic surface partial differential equations (PDEs). The PDE is first written in covariant form using an appropriate local reference system. The knowledge of the local parametrization allows us to consider the two-dimensional VEM scheme, without any explicit approximation of the surface geometry. The theoretical properties of the classical VEM are extended to our framework by taking into consideration the highly anisotropic character of the final discretization. These properties are extensively tested on triangular and polygonal meshes using a manufactured solution. The limitations of the scheme are verified as functions of the regularity of the surface and its approximation.
Identifiants
pubmed: 34803175
doi: 10.1007/s10092-021-00418-5
pii: 418
pmc: PMC8591694
doi:
Types de publication
Journal Article
Langues
eng
Pagination
30Informations de copyright
© The Author(s) 2021.
Références
Numer Math (Heidelb). 2017;137(4):857-893
pubmed: 29151622
Numer Math (Heidelb). 2019;141(1):141-172
pubmed: 30906074