Abstract: The local discontinuous Galerkin (LDG) method using to solve poisson equations on two-dimensional domain was introduced. The construction of LDG was described. The algorithm formulation and practical implementation with linear elements and quadratic elements were discussed in triangular element cases, including numerical quadrature rules, mass matrix formula and iterative methods to solve system. At last, numerical experiments were presented to verify the accuracy of convergence.

Key words: oisson equations, Local discontinuous Galerkin, Unstructured meshes

摘要： 利用局部间断Galerkin(LDG)有限元方法求解二维区域上Poisson方程。介绍了局部间断有限元方法的构造。详细地讨论了该方法在二维三角形网格上的线性元与二次元的算法实现,包括数值积分、质量矩阵公式以及迭代运算求解方程组。最后,给出数值算例,验证了该方法的收敛精度。

关键词: Poisson方程, 局部间断Galerkin, 非结构网格