Robustness and dispersion analysis of the Partition of Unity Finite Element Method applied to the Helmholtz equation

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Autori principali: Hervella-Nieto, Luis María, López Pérez, Paula M., Prieto, Andrés
Natura: Recurso digital
Lingua:inglese
Pubblicazione: Zenodo 2019
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author Hervella-Nieto, Luis María
López Pérez, Paula M.
Prieto, Andrés
author_facet Hervella-Nieto, Luis María
López Pérez, Paula M.
Prieto, Andrés
contents <h3>Abstract: </h3> <p>The Partition of Unity Finite Element Method (PUFEM) has been widely used for the numerical simulation of the Helmholtz equation in different physical settings. In fact, it is a numerical pollution-free alternative method to the classical piecewise polynomial-based finite element methods.<br>Taking into account a plane wave enrichment of the piecewise linear finite element method, the main goal of this work is focused on the derivation of the numerical dispersion relation and the robustness analysis of the PUFEM discretization when a spurious perturbation is presented in the wave number value used in the enrichment definition. From the one-dimensional Helmholtz equation, the discrete wave number is estimated based on a Bloch’s wave analysis and a priori error<br>estimates are computed explicitly in terms of the mesh size, the wave number, and the perturbation value.</p>
format Recurso digital
id zenodo_https___doi_org_10_5281_zenodo_14753350
institution Zenodo
language eng
publishDate 2019
publisher Zenodo
record_format zenodo
spellingShingle Robustness and dispersion analysis of the Partition of Unity Finite Element Method applied to the Helmholtz equation
Hervella-Nieto, Luis María
López Pérez, Paula M.
Prieto, Andrés
Partition of unity finite element method
Discrete dispersion relation
Robustness analysis
<h3>Abstract: </h3> <p>The Partition of Unity Finite Element Method (PUFEM) has been widely used for the numerical simulation of the Helmholtz equation in different physical settings. In fact, it is a numerical pollution-free alternative method to the classical piecewise polynomial-based finite element methods.<br>Taking into account a plane wave enrichment of the piecewise linear finite element method, the main goal of this work is focused on the derivation of the numerical dispersion relation and the robustness analysis of the PUFEM discretization when a spurious perturbation is presented in the wave number value used in the enrichment definition. From the one-dimensional Helmholtz equation, the discrete wave number is estimated based on a Bloch’s wave analysis and a priori error<br>estimates are computed explicitly in terms of the mesh size, the wave number, and the perturbation value.</p>
title Robustness and dispersion analysis of the Partition of Unity Finite Element Method applied to the Helmholtz equation
topic Partition of unity finite element method
Discrete dispersion relation
Robustness analysis
url https://doi.org/10.5281/zenodo.14753350