Details

Autor(en) / Beteiligte

• Dassi, F.
• Di Barba, P.

Titel

Enriched Virtual Element space on curved meshes with an application in magnetics

Ist Teil von

• Computers & mathematics with applications (1987), 2024-05, Vol.161, p.43-50

Ort / Verlag

Elsevier Ltd

Erscheinungsjahr

2024

Quelle

Elsevier ScienceDirect Journals

Beschreibungen/Notizen

• In Beirão da Veiga et al. 2019, the authors proposed a virtual element method for domains with fixed curved boundary that tends to be locally straight when the discretisation gets finer and finer. In this paper, we properly modify this method so that it can also deal with curved mesh edges which are not necessarily located along boundaries and do not tend to be straight when refining the mesh. To achieve this goal, we assume that curved edges are described by polynomials and we increase the dimension of the virtual element space used in Beirão da Veiga et al. 2019. In the numerical experiments, we compare these two methods. Furthermore, we apply the proposed approach to the benchmark “TEAM 25” problem, an optimal shape design problem in magnetostatics characterised by curved edges.