Multiphysics Finite Element Method Based On Nitsche's Method For Stokes-poroelasticity Problem

In the thesis,we study the multiphysics finite element method based on Nitsche's method for Stokes-poroelasticity problem.Firstly,we present a multiphysics reformula-tion of poroelasticity part of the original problem by introducing two pseudo-pressures,which reveals the underlying deformation and diffusion multiphysics process in the Stokes-poroelasticity problem.Then,we define the weak solution of the reformulated problem and prove the existence and uniqueness of weak solution of the original problem and the reformulated problem.We use Nitsche's method to approximate the coupling condition at the interface and analyze the stability of the reformulated full-coupling problem.For the reformulated full-coupling problem,we propose a fully discrete multiphysics finite element method,namely the loosely-coupled time-stepping method,which decouples the problem into three sub-problems at each time step:a Stokes problem,a generalized Stokes prob-lem and a mixed diffusion problem.The loosely-coupled time-stepping method allows to solve each sub-problem of the system independently at each time step.Thus,it greatly reduces the requirements of storage space and improves the computational efficiency and accuracy.So we establish a loosely-coupled time-stepping method with good stability and no "locking phenomenon".Also,we give the stability analysis and error estimates of the loosely-coupled time-stepping method.Finally,we give the numerical test to verify the effectiveness and feasibility of method...