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arXiv · 2310.09260

A lowest order stabilization-free mixed Virtual Element Method

Andrea Borio·Carlo Lovadina·Francesca Marcon·Michele Visinoni
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Abstract

We initiate the design and the analysis of stabilization-free Virtual Element Methods for the laplacian 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.

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Andrea Borio, Carlo Lovadina, Francesca Marcon, Michele Visinoni. 2023-10-13. A lowest order stabilization-free mixed Virtual Element Method. https://arxiv.org/abs/2310.09260

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