Discontinuous Galerkin Method

The Discontinuous Galerkin (DG) method was initially introduced by Reed and Hill in 1973 as a technique to solve neutron transport problems. Lesaint presented the first numerical analysis of the method for a linear advection equation. However, the technique has only recently become popular as a method for solving fluid dynamics or electromagnetic problems.

The Discontinuous Galerkin method is somewhere between a finite element and a finite volume method and has many good features of both. It provides a practical framework for the development of high-order accurate methods using unstructured grids. The method is well suited for large-scale time-dependent computations in which high accuracy is required. An important distinction between the DG method and the usual finite-element method is that in the DG method the resulting equations are local to the generating element. The solution within each element is not reconstructed by looking to neighboring elements. Its compact formulation can be applied near boundaries without specail treatment, which greatly increases the robustness and accuracy of any boundary condition implementation. 

The Discontinuous Galerkin Method can be parallelized. The compact form of the DG method makes it well suited for parallel computer platforms.



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Project Leader: Chi-Wang Shu
Project Members: Jianxian Qiu