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Calcolo
Published in: Calcolo 2/2021

01-06-2021

A priori error analysis for a mixed VEM discretization of the spectral problem for the Laplacian operator

Authors: Felipe Lepe, Gonzalo Rivera

Published in: Calcolo | Issue 2/2021

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Abstract

The aim of the present work is to derive error estimates for the Laplace eigenvalue problem in mixed form, implementing a virtual element method. With the aid of the theory for non-compact operators, we prove that the proposed method is spurious free and convergent. Optimal order of convergence for the eigenvalues and eigenfunctions are derived. Finally, we report numerical tests to confirm the theoretical results together with a rigorous computational analysis of the effects of the stabilization parameter, inherent for the virtual element methods, in the computation of the spectrum.
previous article Improved error estimates for Hybrid High-Order discretizations of Leray–Lions problems
next article A Hermite collocation method for approximating a class of highly oscillatory integral equations using new Gaussian radial basis functions
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Metadata
Title
A priori error analysis for a mixed VEM discretization of the spectral problem for the Laplacian operator
Authors
Felipe Lepe
Gonzalo Rivera
Publication date
01-06-2021
Publisher
Springer International Publishing
Published in
Calcolo / Issue 2/2021
Print ISSN: 0008-0624
Electronic ISSN: 1126-5434
DOI
https://doi.org/10.1007/s10092-021-00412-x

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