求解时间相关Brinkman方程弱有限元方法的误差估计

Error Estimation of Weak Galerkin Finite Element Method for Solving Time-Dependent Brinkman Equation

采用弱有限元方法求解时间相关Brinkman方程.通过仅对空间离散的半离散格式,及对时间和空间均离散的全离散格式分别构造相应的误差方程进行误差分析,得到了速度函数在H1和L2范数,压力函数在H1范数下的最优阶误差估计,从而使弱有限元方法应用更广泛.

We solved time-dependent Brinkman equation by the weak Galerkin finite element method. Corresponding error equations and error estimates were established by using semi-discrete scheme only for the discrete space and full-discrete scheme for the time and space discretization. We obtained the optimal rate convergence in H1 and L2 norm for the velocity function, and in H1 norm for the pressure function. So that the weak Galerkin finite element method was applied more widely.