A virtual element method for the elasticity problem allowing small edges

Amigo, Danilo; Lepe, Felipe; Rivera, Gonzalo

doi:10.48550/arxiv.2211.02792

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2023

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“…This is an ongoing subject of research, and the available results are for VEM spaces to discretize H 1 . Also, recently on [3,20,27,32] is possible to find applications of the small edges approach.…”

Section: Introductionmentioning

confidence: 99%

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

Lepe¹,

Rivera²

2023

Preprint

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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 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.

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Section: Introductionmentioning

confidence: 99%