A stabilization-free Virtual Element Method: main features and an application to a convection-diffusion eigenvalue problem
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In this talk we introduce stabilization-free Virtual Element Methods (VEM), describing the basic ideas of these methods and then focusing in particular on the solution of the non-selfadjoint convection-diffusion eigenvalue problem. Stabilization-free VEM are designed in order to preserve the structure of the model problem, exploiting only polynomial projections in the discrete bilinear forms. First, the talk will cover the main features of stabilization-free VEM applied to the solution of elliptic problems following [1, 2]. Then, we will focus on a convection-diffusion eigenvalue problem, showing that the proposed scheme provides a correct approximation of the spectrum and optimal error estimates for the eigenfunctions and a double order for the eigenvalues. Numerical results will show the robustness of the presented scheme [3]. REFERENCES [1] S. Berrone, A. Borio, F. Marcon, G. Teora, A first-order stabilization-free virtual element method, Applied Mathematics Letters, 2023. [2] S. Berrone, A. Borio, F. Marcon, Comparison of standard and stabilization free virtual elements on anisotropic elliptic problems, Applied Mathematics Letters, 2022. [3] F. Marcon, D. Mora, A stabilization-free virtual element method for the convection-diffusion eigenproblem, To appear.
