Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4634714 | Applied Mathematics and Computation | 2008 | 13 Pages |
Abstract
A discontinuous Galerkin method with interior penalties is presented for nonlinear Sobolev equations. A semi-discrete and a family of Fully-discrete time approximate scheme are formulated. These schemes can be symmetric or nonsymmetric. Hp-version error estimates are analyzed for these schemes. Just because of a damping term â·(b(u)âut) included in Sobolev equation, which is the distinct character different from parabolic equation, special test functions are chosen to deal with this term. Finally, a priori Lâ(H1) error estimate is derived for the semi-discrete time scheme and similarly, lâ(H1) and l2(H1) for the Fully-discrete time schemes. These results also indicate that spatial rates in H1 and time truncation errors in L2 are optimal.
Related Topics
Physical Sciences and Engineering
Mathematics
Applied Mathematics
Authors
Tongjun Sun, Danping Yang,