Arbitrary-order intrinsic virtual element method for elliptic equations on surfaces

Publikation: Beitrag in FachzeitschriftForschungsartikelBeigetragenBegutachtung

Beitragende

Abstract

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.

Details

OriginalspracheEnglisch
Aufsatznummer30
Seitenumfang28
FachzeitschriftCalcolo
Jahrgang58
Ausgabenummer3
PublikationsstatusVeröffentlicht - Sept. 2021
Peer-Review-StatusJa

Externe IDs

Scopus 85111378457

Schlagworte

Schlagwörter

  • Geometrically intrinsic operators, Polygonal mesh, Surface PDEs, Virtual element method, high-order methods