Séminaire ACSIOM :

Le 11 février 2025 à 13:15 - salle 109 (1er étage)

Présentée par Rupp Andreas - Saarland University

Multilevel methods for hybrid discretizations

Hybrid discretization methods, such as the Hybrid Discontinuous Galerkin (HDG) and Hybrid High-Order (HHO) methods, offer highly attractive approaches for solving elliptic partial differential equations. They ensure mass conservation, achieve optimal convergence rates, and yield symmetric positive definite discretization matrices, along with several other desirable properties. However, these methods present inherent challenges when constructing mesh-transfer operators, which are essential for multigrid and multiscale techniques (e.g., localized orthogonal decomposition). The difficulty arises because the mesh skeleton (the union of mesh faces) expands with refinement, complicating transfer operations. In this presentation, we introduce the construction of stable mesh-transfer operators and demonstrate their application in multigrid and multiscale methods. Additionally, we define a class of HDG and HHO discretizations whose resulting linear systems can be efficiently solved using our approach.