2021/12/23 by Zhihao Ge, Ge, Zhihao, Jin'ge Pang +3 · 1 citation
Computer Science · Engineering · Mathematics · #65N30 #Advanced Mathematical Modeling in Engineering #Advanced Numerical Methods in Computational Mathematics #Analysis of PDEs (math.AP) #Differential Equations and Numerical Methods #FOS: Mathematics #G.1.8 #Numerical Analysis (math.NA)
paper · pdf · doi:10.48550/arxiv.2112.12421
openalex publication_date 2021/12/23 · openalex created_date 2022/10/07 · openalex updated_date 2026/07/28
In this paper, we propose a multiphysics mixed finite element method with Nitsche's technique for Stokes-poroelasticity problem. Firstly, we present a multiphysics reformulation of poroelasticity part of the original problem by introducing two pseudo-pressures to reveal the underlying deformation and diffusion multi physical processes in the Stokes-poroelasticity problem. Then, we prove the existence and uniqueness of weak solution of the reformulated and original problem. And we use Nitsche's technique to approximate the coupling condition at the interface to propose a loosely-coupled time-stepping method -- multiphysics mixed finite element method for space variables, and we decouple the reformulated problem into three sub-problems at each time step -- a Stokes problem, a generalized Stokes problem and a mixed diffusion problem. Also, we give the stability analysis and error estimates of the loosely-coupled time-stepping method.