The Discontinuous Galerkin Method

Accuracy preserving and nonoscillatory shock capturing technique is one of the bottlenecks in the development of discontinuous Galerkin method. In this chapter, a new limiter based on the secondary reconstruction and WENO approach in characteristic space is developed for the discontinuous Galerkin method. Specifically, the efficient secondary reconstruction technique is adopted to provide the candidate polynomials used in the weighted average procedure of the WENO approach. The secondary reconstructions are performed only on the face neighboring cells to keep the compactness of the discontinuous Galerkin method.

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