The Nonconforming Trefftz Virtual Element Method: General Setting, Applications, and Dispersion Analysis for the Helmholtz Equation

Lorenzo Mascotto; Ilaria Perugia; Alexander Pichler

doi:https://arxiv.org/abs/2102.11581

The Nonconforming Trefftz Virtual Element Method: General Setting, Applications, and Dispersion Analysis for the Helmholtz Equation

Lorenzo Mascotto (Korresp. Autor*in), Ilaria Perugia, Alexander Pichler

Institut für Mathematik

Veröffentlichungen: Beitrag in Buch › Beitrag in Buch/Sammelband › Peer Reviewed

Abstract

We present a survey of the nonconforming Trefftz virtual element method for the Laplace and Helmholtz equations. For the latter, we present a new abstract analysis, based on weaker assumptions on the stabilization, and numerical results on the dispersion analysis, including comparison with the plane wave discontinuous Galerkin method.

Originalsprache	Englisch
Titel	The Virtual Element Method and its Applications
Redakteure*innen	Paola F. Antonietti, Lourenco Beirao da Veiga, Gianmarco Manzini
Erscheinungsort	Cham
Herausgeber (Verlag)	Springer
Seiten	363-410
ISBN (elektronisch)	978-3-030-95319-5
ISBN (Print)	978-3-030-95318-8
DOIs	https://doi.org/https://arxiv.org/abs/2102.11581 https://doi.org/10.1007/978-3-030-95319-5_9
Publikationsstatus	Veröffentlicht - Okt. 2022

Publikationsreihe

Reihe	SEMA SIMAI Springer Series
Band	31
ISSN	2199-3041

ÖFOS 2012

101014 Numerische Mathematik

Zugriff auf Dokument

Andere Dateien und Links

http://www.scopus.com/inward/record.url?eid=2-s2.0-85102539695&partnerID=MN8TOARS

Zitationsweisen

Mascotto, L., Perugia, I., & Pichler, A. (2022). The Nonconforming Trefftz Virtual Element Method: General Setting, Applications, and Dispersion Analysis for the Helmholtz Equation. in P. F. Antonietti, L. B. da Veiga, & G. Manzini (Hrsg.), The Virtual Element Method and its Applications (S. 363-410). Springer. SEMA SIMAI Springer Series Band 31 https://doi.org/https://arxiv.org/abs/2102.11581, https://doi.org/10.1007/978-3-030-95319-5_9

Mascotto, Lorenzo ; Perugia, Ilaria ; Pichler, Alexander. / The Nonconforming Trefftz Virtual Element Method: General Setting, Applications, and Dispersion Analysis for the Helmholtz Equation. The Virtual Element Method and its Applications. Hrsg. / Paola F. Antonietti ; Lourenco Beirao da Veiga ; Gianmarco Manzini. Cham : Springer, 2022. S. 363-410 (SEMA SIMAI Springer Series, Band 31).

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abstract = "We present a survey of the nonconforming Trefftz virtual element method for the Laplace and Helmholtz equations. As for the latter, we show a new abstract analysis, based on weaker assumptions on the stabilization, and numerical results on the dispersion analysis, including comparison with the plane wave discontinuous Galerkin method.",

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Mascotto, L, Perugia, I & Pichler, A 2022, The Nonconforming Trefftz Virtual Element Method: General Setting, Applications, and Dispersion Analysis for the Helmholtz Equation. in PF Antonietti, LB da Veiga & G Manzini (Hrsg.), The Virtual Element Method and its Applications. Springer, Cham, SEMA SIMAI Springer Series, Bd. 31, S. 363-410. https://doi.org/https://arxiv.org/abs/2102.11581, https://doi.org/10.1007/978-3-030-95319-5_9

The Nonconforming Trefftz Virtual Element Method: General Setting, Applications, and Dispersion Analysis for the Helmholtz Equation. / Mascotto, Lorenzo (Korresp. Autor*in); Perugia, Ilaria; Pichler, Alexander.

The Virtual Element Method and its Applications. Hrsg. / Paola F. Antonietti; Lourenco Beirao da Veiga; Gianmarco Manzini. Cham : Springer, 2022. S. 363-410 (SEMA SIMAI Springer Series, Band 31).

Veröffentlichungen: Beitrag in Buch › Beitrag in Buch/Sammelband › Peer Reviewed

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Mascotto L, Perugia I, Pichler A. The Nonconforming Trefftz Virtual Element Method: General Setting, Applications, and Dispersion Analysis for the Helmholtz Equation. in Antonietti PF, da Veiga LB, Manzini G, Hrsg., The Virtual Element Method and its Applications. Cham: Springer. 2022. S. 363-410. (SEMA SIMAI Springer Series, Band 31). doi: https://arxiv.org/abs/2102.11581, https://doi.org/10.1007/978-3-030-95319-5_9