English

A lowest order stabilization-free mixed Virtual Element Method

Numerical Analysis 2023-10-16 v1 Numerical Analysis

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.

Keywords

Cite

@article{arxiv.2310.09260,
  title  = {A lowest order stabilization-free mixed Virtual Element Method},
  author = {Andrea Borio and Carlo Lovadina and Francesca Marcon and Michele Visinoni},
  journal= {arXiv preprint arXiv:2310.09260},
  year   = {2023}
}
R2 v1 2026-06-28T12:50:07.738Z