Error estimates for shock capturing finite element approximations of the one dimensional Burgers' equation
Numerical Analysis
2014-05-09 v3
Abstract
We propose an error analysis in weak norms of a shock capturing finite element method for the Burgers' equation. The estimates can be related to estimates of certain filtered quantities and are robust in the inviscid limit. Using a total variation apriori bound on the discrete solution and an interpolation inequality error estimates in -norms can are obtained using interpolation.
Keywords
Cite
@article{arxiv.1111.1182,
title = {Error estimates for shock capturing finite element approximations of the one dimensional Burgers' equation},
author = {Erik Burman},
journal= {arXiv preprint arXiv:1111.1182},
year = {2014}
}
Comments
22 pages