Enhanced accuracy by post-processing for finite element methods for hyperbolic equations.

Journal article

We consider the enhancement of accuracy, by means of a simple post-processing technique, for finite element approximations to transient hyperbolic equations. The post-processing is a convolution with a kernel whose support has measure of order one in the case of arbitrary unstructured meshes; if the mesh is locally translation invariant, the support of the kernel is a cube whose edges are of size of the order of Δx only. For example, when polynomials of degree k are used in the discontinuous Galerkin (DG) method, and the exact solution is globally smooth, the DG method is of order k + 1/2 in the L 2-norm, whereas the post-processed approximation is of order 2k + 1; if the exact solution is in L 2 only, in which case no order of convergence is available for the DG method, the post-processed approximation converges with order k + 1/2 in L 2 (Ω 0), where Ω 0 is a subdomain over which the exact solution is smooth. Numerical results displaying the sharpness of the estimates are presented.

Authors: Cockburn, B; Luskin, M; Shu, C; Süli, E

• Publication status: Published
• Journal: Math. Comput.
• Volume: 72
• Issue: 242
• Pages: 577-606
• Publication date: 2003-01-01
• DOI: 10.1090/S0025-5718-02-01464-3
• ISSN: 0025-5718
• Language: English
• Keywords: hyperbolic problems; post-processing; finite element methods