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Mathematics > Numerical Analysis

arXiv:2302.02240 (math)
[Submitted on 4 Feb 2023]

Title:VEM discretization allowing small edges for the reaction-convection-diffusion equation: source and spectral problems

Authors:Felipe Lepe, Gonzalo Rivera
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Abstract:In this paper we analyze a lowest order virtual element method for the load classic 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 for the eigenvalues and eigenfunctions. We report numerical tests to assess the performance of the small edges on our numerical method for both problems under consideration.
Subjects: Numerical Analysis (math.NA)
Cite as: arXiv:2302.02240 [math.NA]
  (or arXiv:2302.02240v1 [math.NA] for this version)
  https://doi.org/10.48550/arXiv.2302.02240

Submission history

From: Gonzalo Rivera [view email]
[v1] Sat, 4 Feb 2023 21:03:34 UTC (15,966 KB)
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