A first-order stabilization-free Virtual Element Method
Stefano Berrone, Andrea Borio, Francesca Marcon, Gioana Teora
TL;DR
This paper presents a novel first-order Virtual Element Method that eliminates the need for stabilization, using a modified diffusion operator to ensure stability while preserving the properties of the differential operator.
Contribution
The paper introduces a stabilization-free VEM based on a modified diffusion operator, simplifying implementation and potentially improving stability and accuracy.
Findings
The method is stable without stabilization terms.
It preserves the properties of the differential operator.
The approach simplifies the VEM formulation.
Abstract
In this paper, we introduce a new Virtual Element Method (VEM) not requiring any stabilization term based on the usual enhanced first-order VEM space. The new method relies on a modified formulation of the discrete diffusion operator that ensures stability preserving all the properties of the differential operator.
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Taxonomy
TopicsAdvanced Numerical Methods in Computational Mathematics · Electromagnetic Simulation and Numerical Methods · Numerical methods for differential equations