| Issue |
ESAIM: M2AN
Volume 57, Number 5, September-October 2023
|
|
|---|---|---|
| Page(s) | 3139 - 3164 | |
| DOI | https://doi.org/10.1051/m2an/2023069 | |
| Published online | 27 October 2023 | |
VEM discretization allowing small edges for the reaction–convection–diffusion equation: source and spectral problems
1
GIMNAP-Departamento de Matemática, Universidad del Bío-Bío, Casilla 5-C, Concepción, Chile
2
Departamento de Ciencias Exactas, Universidad de Los Lagos, Osorno, Chile
* Corresponding author: flepe@ubiobio.cl
Received:
8
February
2023
Accepted:
13
August
2023
In this paper we analyze a lowest order virtual element method for the classic load reaction–convection–diffusion problem and the convection–diffusion spectral problem, where the assumptions on the polygonal meshes allow to consider small edges for the polygons. Under well defined seminorms depending on a suitable stabilization for this geometrical approach, we derive the well posedness of the numerical scheme and error estimates for the load problem, whereas for the spectral problem we derive convergence and error estimates fo the eigenvalues and eigenfunctions. We report numerical tests to asses the performance of the small edges on our numerical method for both problems under consideration.
Mathematics Subject Classification: 49K20 / 49M25 / 65N12 / 65N15 / 65N25 / 65N30
Key words: Virtual element methods / a priori error estimates / small edges
© The authors. Published by EDP Sciences, SMAI 2023
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.