Serendipity Virtual Elements on Polyhedral Meshes
Lourenco Beirao da Veiga, Franco Brezzi, Franco Dassi, Luisa, Donatella Marini, Alessandro Russo
TL;DR
This paper numerically validates the Virtual Element Method (VEM) of order k for 3D elliptic problems with variable coefficients and explores the Serendipity VEM's computational efficiency in reducing degrees of freedom.
Contribution
It provides the first numerical validation of 3D Serendipity VEM and quantifies its computational advantages over standard VEM.
Findings
Serendipity VEM reduces degrees of freedom compared to standard VEM.
Validated the accuracy of VEM for 3D elliptic problems.
Demonstrated computational gains with Serendipity VEM.
Abstract
We numerically validate the Virtual Element Method of order k for general second order elliptic problems with variable coefficients in three dimensions. Moreover, we investigate numerically also the Serendipity version of the VEM (in three dimensions) and the associated computational gain in terms of degrees of freedom.
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Taxonomy
TopicsAdvanced Numerical Methods in Computational Mathematics · Numerical methods in engineering · Electromagnetic Simulation and Numerical Methods