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The conforming virtual element method for polyharmonic and elastodynamics problems: a review

02/02/2021

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by Paola Francesca Antonietti, et al.

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In this paper, we review recent results on the conforming virtual element approximation of polyharmonic and elastodynamics 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 paper. 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.

Paola Francesca Antonietti
10 publications
Gianmarco Manzini
22 publications
Ilario Mazzieri
12 publications
Simone Scacchi
15 publications
Marco Verani
15 publications

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