Analysis of a preconditioner for a membrane diffusion problem with the Kedem–Katchalsky transmission condition. (15th September 2022)

• Record Type: Journal Article
• Authors: Krzyżanowski, Piotr
• Is Part Of: Computers & mathematics with applications. Volume 122(2022)
• Page Start: 28
• Page End: 34
• Publication Date: 2022-09-15
• Subjects: Kedem–Katchalsky condition -- Preconditioner -- Discontinuous Galerkin; Electronic data processing -- Periodicals; Mathematics -- Data processing -- Periodicals; 510.28541
• DOI: 10.1016/j.camwa.2022.07.008
• Languages: English
• ISSNs: 0898-1221

Abstract

Abstract: A composite h - p discontinuous Galerkin finite element discretization of a diffusion problem, where subdomains are separated by thin membranes, modeled by the Kedem–Katchalsky transmission condition, is considered. A preconditioner based on the additive Schwarz method is proved to have the condition number bounded independently of the mesh size, the membrane permeability and the diffusion coefficient, provided the subspace solvers have their condition numbers bounded as well. Numerical experiments confirm these findings and additionally indicate the convergence rate is only weakly dependent on the degree of the approximating polynomials.