Virtual Element Method for Second Order Elliptic Eigenvalue Problems
Francesca Gardini, Giuseppe Vacca
TL;DR
This paper introduces the Virtual Element Method (VEM) for solving second order elliptic eigenvalue problems, demonstrating optimal approximation of eigenmodes through theoretical analysis and numerical tests.
Contribution
The paper presents a novel application of VEM to elliptic eigenvalue problems, establishing optimal approximation properties and validating them with numerical experiments.
Findings
VEM achieves optimal order approximation of eigenmodes.
Numerical tests confirm the theoretical convergence rates.
VEM is effective for elliptic eigenvalue problems.
Abstract
We introduce the Virtual Element Method (VEM) for elliptic eigenvalue problems. The main result of the paper states that VEM provides an optimal order approximation of the eigenmodes. A wide set of numerical tests confirm the theoretical analysis.
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Taxonomy
TopicsAdvanced Numerical Methods in Computational Mathematics · Numerical methods in engineering · Electromagnetic Simulation and Numerical Methods