2024/04/25 by Stefan Meggendorfer, Guido Kanschat, Meggendorfer, Stefan +3 · 1 citation
Computer Science · Engineering · Physics and Astronomy · #65F10 #65M12 #65M55 #Advanced Numerical Methods in Computational Mathematics #Electromagnetic Scattering and Analysis #FOS: Mathematics #Matrix Theory and Algorithms #Numerical Analysis (math.NA)
paper · pdf · doi:10.48550/arxiv.2404.16684
openalex publication_date 2024/04/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper addresses the construction and analysis of a class of domain decomposition methods for the iterative solution of the quasi-static Biot problem in three-field formulation. The considered discrete model arises from time discretization by the implicit Euler method and space discretization by a family of strongly mass-conserving methods exploiting Hdiv-conforming approximations of the solid displacement and fluid flux fields. For the resulting saddle-point problem, we construct monolithic overlapping domain decomposition (DD) methods whose analysis relies on a transformation into an equivalent symmetric positive definite system and on stable decompositions of the involved finite element spaces under proper problem-dependent norms. Numerical results on two-dimensional test problems are in accordance with the provided theoretical uniform convergence estimates for the two-level multiplicative Schwarz method.