Issue |
ESAIM: M2AN
Volume 59, Number 1, January-February 2025
|
|
---|---|---|
Page(s) | 363 - 387 | |
DOI | https://doi.org/10.1051/m2an/2024081 | |
Published online | 08 January 2025 |
Nodal auxiliary space preconditioners for mixed virtual element methods
1
NORCE Norwegian Research Centre, N-5838 Bergen, Norway
2
Department of Mathematics, KTH Royal Institute of Technology, SE-100 44 Stockholm, Sweden
* Corresponding author: erikni6@kth.se
Received:
19
April
2024
Accepted:
10
November
2024
We propose nodal auxiliary space preconditioners for facet and edge virtual elements of lowest order by deriving discrete regular decompositions on polytopal grids and generalizing the Hiptmair–Xu preconditioner to the virtual element framework. The preconditioner consists of solving a sequence of elliptic problems on the nodal virtual element space, combined with appropriate smoother steps. Under assumed regularity of the mesh, the preconditioned system is proven to have bounded spectral condition number independent of the mesh size and this is verified by numerical experiments on a sequence of polygonal meshes. Moreover, we observe numerically that the preconditioner is robust on meshes containing elements with high aspect ratios.
Mathematics Subject Classification: 65N30 / 65N85 / 65N22
Key words: Auxiliary space preconditioning / Hiptmair–Xu preconditioner / mixed virtual element methods
© The authors. Published by EDP Sciences, SMAI 2025
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