Enhanced Accuracy by Post-processing for Finite Element Methods for Hyperbolic Equations
INSTITUTE FOR COMPUTER APPLICATIONS IN SCIENCE AND ENGINEERING HAMPTON VA
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Abstract. We consider the enhancement of accuracy, by means of a simple post-processing technique, for nite 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 the mesh size 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 12 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 12 inL 2 over a subdomain on which the exact solution is smooth. Numerical results displaying the sharpness of the estimates are presented.
- Numerical Mathematics