针对一类带有非对角扩散变张量系数的广义自共轭椭圆问题导出的偏微分系统,给出了椭圆问题在三角剖分下的扩展混合体积元方法。该方法在三角单元上采用了最低次的R—T扩展混合元空间,得到近似压力、近似速度以及近似通量的拟最优误差估计。
An expanded mixed cobolume method for a system of firstorder PDEs resulting from the mixed formulation of a general self-adjoint elliptic problem with a full diffusion tensor on triangular grids is presented. The lowest order R - T mixed element space on triangular grids is used. Optimal rate of convergence for approximate pressure, as well as for approximate velocity and it's flux( the coefficient times the gradient) is obtained for this formulation.