A Stabilized Crank-Nicolson Leap-Frog Method For Time-dependent Stokes-Darcy Model

The Stokes-Darcy model is a mathematical-physical model that simulates the permeation of free fluids in a porous medium,which is often widely used in engineering.It is a coupled system of partial differential equations with high complexity,and the study of the stability,efficiency,and precision of its numerical format has always been an important topic in the field of computational mathematics.A stabilized Crank-Nicolson LeapFrog(SCNLF)method for the non-stationary StokesDarcy model is presented and analyzed.The idea of the method is to combine the CNLF method with the stabilized method to solve the decoupled model by using the the lowest-order finite element pairs.As the lowest order finite element pairs lead to the loss of LBB condition,the stabilization approach is used to counteract this deficiency.In this method,the coupled model is divided into two sub-problem:one is non-stationary Stokes equations solved by SCNLF method,and the other one is non-stationary Darcy equations solved by CNLF.Stability and the optimal error estimate of the numerical method are proved.Finally,some numerical tests are presented to justify the theoretical result.