Extension of a Post-Processing Technique for the
Discontinuous
Galerkin Method
Presented
by:
Jennifer K.
Ryan
Householder
Postdoctoral Fellow
Computer
Science and Mathematics Division
Abstract:
Cockburn,
Luskin, Shu, and Suli previously introduced a post-processing technique for the
discontinuous Galerkin method that allows improvement in accuracy from
order k+1 to order 2k+1 for linear hyperbolic equations. This technique
is based on negative order norm estimates. A uniform mesh assumption
allows for simple implementation via small matrix-vector multiplications.
In this talk, we present extensions of this improvement in accuracy to include
superconvergence of the derivatives, variable coefficient hyperbolic equations,
one-sided post-processing, and post-processing over a smoothly varying mesh.