扩散反应方程的一种协调间断有限元法

对于定常扩散反应方程的原始混合变分形式，本文基于间断有限元法和最小二乘法思想给出了一种新的协调间断有限元格式，并将其推广应用于非定常扩散反应方程，进而建立了一个全离散协调间断有限元格式. 该格式不仅能避免LBB条件，而且适用于多边形网格. 在能量范数下，本文获得了原始变量和通量的最优收敛阶误差估计. 最后，针对定常和非定常的扩散反应方程，本文分别以一般情形和对流占优情形下的数值算例验证了方法的有效性.

A conforming discontinuous finite element method for diffusion-reaction equations

For the primal-mixed form of the steady diffusion-reaction equation, a new conforming discontinuous finite element scheme is proposed by using the idea of discontinuous finite element method and the least-square method. Then the method is extended to the case of unsteady diffusion-reaction diffusion equation and a fully comforming discontinuous finite element scheme is given. This scheme avoids the LBB condition and can be applied to polygon mesh. Under the energy norm, the optimal convergence order for the primary and flux variables are estabilished. Finally, for the steady and unsteady diffusion reaction equations, some numerical examples in general and reaction dominated cases are given to verify the effectiveness of the method.