二维热传导方程的局部间断Galerkin有限元方法

Local Discontinuous Galerkin Method for the Two-Dimensional Heat Equation

讨论了局部间断Galerkin有限元方法求解二维热传导方程。通过引入辅助变量将含有二阶导数的热传导方程重新写为一阶偏微分方程组,在空间上用间断有限元离散得到一组常微分方程组,在时间上用显式方法离散,最终给出数值算例验证了该方法的收敛精度。

The local discontinuous Galerkin method for the two--dimensional equation was introduced. By introducing the auxiliary variable, the second derivative heat conduction equation equations were rewritten into first--order partial differential equations, then the discontinuous Galerkin method was applied to the system. Finally the method yields ordinary differential equations systems. The explicit method was used for the time discretization. The numerical experiments were presented to verify the accuracy of the method.