Stabilization-free Virtual Element Method for 2D second order elliptic equations

In this work, we present and analyze a Stabilization-free Virtual Element high order scheme for 2D second order elliptic equation. This method is characterized by the definition of new polynomial projections that allow the definition of structure-preserving schemes. We provide a necessary and suffic...

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Bibliographic Details
Published in:Computer methods in applied mechanics and engineering Vol. 438; p. 117839
Main Authors: Berrone, Stefano, Borio, Andrea, Fassino, Davide, Marcon, Francesca
Format: Journal Article
Language:English
Published: Elsevier B.V 01.04.2025
Subjects:
Polygonal meshes
RCD problems
Structure-preserving formulation
Virtual Element Methods
65N15
65N12
Structure-preserving formulation
Polygonal meshes
RCD problems
65N30
Virtual Element Methods
ISSN:0045-7825
Online Access:Get full text
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Summary:In this work, we present and analyze a Stabilization-free Virtual Element high order scheme for 2D second order elliptic equation. This method is characterized by the definition of new polynomial projections that allow the definition of structure-preserving schemes. We provide a necessary and sufficient condition on the polynomial projection space that ensure the well-posedness of the scheme and we derive optimal a priori error estimates. Several numerical tests assess the stability of the method and the robustness in solving problems characterized by anisotropies. •Virtual Element method without an arbitrary stabilization.•Structure preserving bilinear form for 2D second order elliptic equations.•Well-posedness analysis.•Algorithm for the computation of coercive polynomial projection.•Numerical tests assessing local coercivity on several polygons, and good performance on anisotropic diffusion problems.
ISSN:0045-7825
DOI:10.1016/j.cma.2025.117839