极坐标系下Poisson方程的局部间断有限元方法

Local Discontinuous Galerkin Method for the Poisson Equation in Polar Coordinates

考虑圆形、扇形等区域上的Poisson方程的局部间断有限元方法 ,给出了极坐标系下Poisson方程的局部间断有限元格式并给出了数值实验结果。如果所求解的问题充分光滑,数值实验表明:在k次间断有限元空间求解时,原始变量的误差阶可以达到k+1阶,而辅助变量的误差阶可达到k阶。

In this paper we consider the LDG method for the Poisson equation in disk or fan-shaped domain. Numerical scheme is given for the LDG method and numerical experiments are implemented also. Numerical results show that when the problem considered is sufficiently smooth, （k＋1）-th order of convergence for the primal variable, k-th order of convergence for the auxiliary variable can be obtained if the k-th order discontinuous polynomial space is used.