Diego Paredes, Frederic Valentin, Henrique M. Versieux:
Revisiting the robustness of the multiscale hybrid-mixed method: the face-based strategy
This work proposes a new finite element for the mixed multiscale hybrid method (MHM) applied to the Poisson equation with highly oscillatory coefficients. Unlike the original MHM method, multiscale bases are the solution to local Neumann problems driven by piecewise continuous polynomial interpolation on the skeleton faces of the macroscale mesh. As a result, we prove the optimal convergence of MHM by refining the face partition and leaving the mesh of macroelements fixed. This strategy allows the MHM method to be resonance free under the usual assumptions of local regularity. The numerical analysis of the method also revisits and complements the original approach proposed by D. Paredes, F. Valentin and H. Versieux (2017). A numerical experiment evaluates the new theoretical results.
This preprint gave rise to the following definitive publication(s):
Diego PAREDES, Frederic VALENTIN, Henrique M. VERSIEUX: Revisiting the robustness of the multiscale hybrid-mixed method: the face-based strategy. Journal of Computational and Applied Mathematics, vol. 436, article: 115415, (2024).