Print Email Facebook Twitter Local derivative post-processing: Challenges for a non-uniform mesh Title Local derivative post-processing: Challenges for a non-uniform mesh Author Ryan, J.K. Faculty Electrical Engineering, Mathematics and Computer Science Department Delft Institute of Applied Mathematics Date 2010-08-20 Abstract Previous investigations into accuracy enhancement for the derivatives of a discontinuous Galerkin solution demonstrated that there are many ways to approach obtaining higher order accuracy in the derivatives, each with different advantageous properties. For the discontinuous Galerkin method, the order of accuracy without post-processing for the dth?derivative is k+1-d. For the derivative of the post-processed solution it is 2k+1-d. Additionally, it was demonstrated that not only is calculating the derivative of the post-processed solution itself unnecessary, but also that order 2k+1 can be obtained for the derivative solution for any order derivative, provided the solution is 2k+1 continuous. This is done using higher-order B-splines than used for the post-processed solution itself convolved against a finite difference derivative. This introduces higher levels of smoothness into the derivative post-processed approximation. However, this investigation was limited to a uniform mesh consideration, which is highly restrictive for practical applications. In this report, we discuss the advantages and disadvantages of extending accuracy enhancement of derivatives to non-uniform meshes in one-dimension using the ideas of local L2-projection, characteristic length as well as direct implementation as done for the post-processed solution itself. Subject accuracy enhancementdiscontinuous Galerkinpost-processingderivativeshyperbolic equations To reference this document use: http://resolver.tudelft.nl/uuid:6f288447-543c-4a08-9c98-d8520dec0646 ISSN 1389-6520 Source Reports of the Delft Institute of Applied Mathematics, 1-18 Part of collection Institutional Repository Document type report Rights (c) 2010 Ryan, J.K. Files PDF jkryan_tudelft_10-18.pdf 218.71 KB Close viewer /islandora/object/uuid:6f288447-543c-4a08-9c98-d8520dec0646/datastream/OBJ/view