FETI-DP for the three-dimensional Virtual Element Method

Abstract

We deal with the Finite Element Tearing and Interconnecting Dual Primal (FETI-DP) preconditioner for elliptic problems discretized by the virtual element method (VEM). We extend the result of [22] to the three dimensional case. We prove polylogarithmic condition number bounds, independent of the number of subdomains, the mesh size, and jumps in the diffusion coefficients. Numerical experiments validate the theory

arXiv comment35 pages

References in corpus (5)

• On the Virtual Element Method for Three-Dimensional Elasticity Problems on Arbitrary Polyhedral Meshes
• A Virtual Element Method for elastic and inelastic problems on polytope meshes
• BDDC and FETI-DP for the Virtual Element Method
• Virtual Element Method for the Laplace-Beltrami equation on surfaces
• BDDC and FETI-DP under Minimalist Assumptions

Cited by in corpus (3)

• Weakly imposed Dirichlet boundary conditions for 2D and 3D Virtual Elements
• Reduced basis stabilization and post-processing for the virtual element method
• Parallel block preconditioners for virtual element discretizations of the time-dependent Maxwell equations