Research On Finite Element Method For The Darcy-Brinkman Equation

Based on the finite element method,this paper constructs the modified charac-teristics method and the decoupled method with different time steps for the time-dependent Darcy-Brinkman equation.Firstly,the modified characteristics finite element method is adapted to deal with the double diffusion problem.And the modified characteristics method is em-ployed to compute the nonlinear terms and times term,then,the decoupling skill is used for calculating the velocity,the pressure,the temperature and the concen-tration.The corresponding stability analysis and the error estimate is given in the paper,and some numerical tests are given,which prove the effectiveness of the modified characteristics finite element method.Secondly,we construct a decoupled finite element method with different time steps for the nonstationary Darcy-Brinkman equation.The main idea of the method is to use decoupled technique to calculate velocity,pressure,temperature and con-centration,and then to adopt the small time step for velocity and pressure,for temperature and concentration,a large time step is used.In addition,we give the stability analysis and error estimation of the method.Then,we give some numerical tests,we can find that the decoupled finite element method with different time steps can save computational time compared with the standard coupling algorithm.