The conforming virtual element method for polyharmonic and elastodynamics problems: a review
Paola Francesca Antonietti, Gianmarco Manzini, Ilario Mazzieri, Simone, Scacchi, Marco Verani
TL;DR
This review discusses recent advances in the conforming virtual element method for solving polyharmonic and elastodynamics problems, highlighting applications in phase field models and fracture mechanics.
Contribution
It provides a comprehensive overview of the mathematical formulation and recent developments in conforming virtual element approximations for complex PDEs.
Findings
Effective approximation of polyharmonic problems
Application to Cahn-Hilliard and elastodynamics
Insights into phase field models for fracture
Abstract
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.
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Taxonomy
TopicsSolidification and crystal growth phenomena · Advanced Mathematical Modeling in Engineering · Advanced Numerical Methods in Computational Mathematics