We initiate the design and the analysis of stabilization-free Virtual Element Methods for the Poisson problem written in mixed form. A Virtual Element version of the lowest order Raviart-Thomas Finite Element is considered. To reduce the computational costs, a suitable projection on the gradients of harmonic polynomials is employed. A complete theoretical analysis of stability and convergence is developed in the case of quadrilateral meshes. Some numerical tests highlighting the actual behaviour of the scheme are also provided.

A lowest order stabilization-free mixed Virtual Element Method / A. Borio, C. Lovadina, F. Marcon, M. Visinoni. - In: COMPUTERS & MATHEMATICS WITH APPLICATIONS. - ISSN 0898-1221. - 160:(2024), pp. 161-170. [10.1016/j.camwa.2024.02.024]

A lowest order stabilization-free mixed Virtual Element Method

C. Lovadina
Secondo
;
M. Visinoni
Ultimo
2024

Abstract

We initiate the design and the analysis of stabilization-free Virtual Element Methods for the Poisson problem written in mixed form. A Virtual Element version of the lowest order Raviart-Thomas Finite Element is considered. To reduce the computational costs, a suitable projection on the gradients of harmonic polynomials is employed. A complete theoretical analysis of stability and convergence is developed in the case of quadrilateral meshes. Some numerical tests highlighting the actual behaviour of the scheme are also provided.
Mixed formulation; Poisson problem; Quadrilateral meshes; Virtual element method
Settore MAT/08 - Analisi Numerica
   Advanced polyhedral discretisations of heterogeneous PDEs for multiphysics problems
   MINISTERO DELL'ISTRUZIONE E DEL MERITO
   20204LN5N5_004

   Virtual Element Methods: Analysis and Applications
   MINISTERO DELL'ISTRUZIONE E DEL MERITO
   201744KLJL_005
2024
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2434/1053796
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