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In this chapter we review recent results on the conforming virtual element approximation of polyharmonic and eleastodynamics problems. The structure and the content of this review is motivated by three paradigmatic examples of applications: classical and anisotropic Cahn-Hilliard equation and phase field models for brittle fracture, that are briefly discussed in the first part of the chapter. We present and discuss the mathematical details of the conforming virtual element approximation of linear polyharmonic problems, the classical Cahn-Hilliard equation and linear elastodynamics problems.

The Conforming Virtual Element Method for Polyharmonic and Elastodynamics Problems: A Review / P.F. Antonietti, G. Manzini, I. Mazzieri, S. Scacchi, M. Verani (SEMA SIMAI SPRINGER SERIES). - In: The Virtual Element Method and its Applications / [a cura di] P. F. Antonietti, L. Beirão da Veiga, G. Manzini. - [s.l] : Springer, 2022. - ISBN 978-3-030-95318-8. - pp. 411-451 [10.1007/978-3-030-95319-5_10]

The Conforming Virtual Element Method for Polyharmonic and Elastodynamics Problems: A Review

S. Scacchi
Penultimo
;M. Verani
Ultimo
2022

Abstract

In this chapter we review recent results on the conforming virtual element approximation of polyharmonic and eleastodynamics problems. The structure and the content of this review is motivated by three paradigmatic examples of applications: classical and anisotropic Cahn-Hilliard equation and phase field models for brittle fracture, that are briefly discussed in the first part of the chapter. We present and discuss the mathematical details of the conforming virtual element approximation of linear polyharmonic problems, the classical Cahn-Hilliard equation and linear elastodynamics problems.
No
English
Settore MAT/08 - Analisi Numerica
Capitolo o Saggio
Esperti anonimi
Pubblicazione scientifica
   Virtual Element Methods: Analysis and Applications
   MINISTERO DELL'ISTRUZIONE E DEL MERITO
   201744KLJL_005
The Virtual Element Method and its Applications
P. F. Antonietti, L. Beirão da Veiga, G. Manzini
Springer
2022
8-mag-2022
411
451
41
978-3-030-95318-8
978-3-030-95319-5
31
Volume a diffusione internazionale
No
scopus
crossref
2-s2.0-85139873818
Aderisco
P.F. Antonietti, G. Manzini, I. Mazzieri, S. Scacchi, M. Verani
Book Part (author)
partially_open
268
The Conforming Virtual Element Method for Polyharmonic and Elastodynamics Problems: A Review / P.F. Antonietti, G. Manzini, I. Mazzieri, S. Scacchi, M. Verani (SEMA SIMAI SPRINGER SERIES). - In: The Virtual Element Method and its Applications / [a cura di] P. F. Antonietti, L. Beirão da Veiga, G. Manzini. - [s.l] : Springer, 2022. - ISBN 978-3-030-95318-8. - pp. 411-451 [10.1007/978-3-030-95319-5_10]
info:eu-repo/semantics/bookPart
5
Prodotti della ricerca::03 - Contributo in volume
03 - Contributo in volume
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2434/965581
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