Post-processing for Discontinuous Galerkin Method:Challenging the Assumption of Uniformity
摘要：Previous investigations into accuracy enhancement for a discontinuous Galerkin solution demonstrated that there are many ways to approach obtaining higher-order accuracy in the solution, for example, the post-processing technique. For the discontinuous Galerkin method, the order of accuracy without post-processing is k+1. For the post-processed solution, it is 2k+1. Additionally, the post-processing introduces higher levels of smoothness into the new approximation. However, previous investigations were mainly limited to uniform meshes (or nearly uniform meshes) consideration, which is highly restrictive for practical application. In this talk, we discuss the challenges and difficulties for non-uniform meshes. Additionally, we present several common techniques of post-processing for non-uniform meshes will be introduced. Moreover, we purpose a new technique which considers the mesh structure as a parameter when dealing the non-uniform meshes. A comparison is made among these techniques through numerical examples.
20171106李小舟Post-processing for Discontinuous Galerkin Method：Challenging the Assumption of Uniformity