@Article{JCM-26-689, author = {}, title = {The Optimal Convergence Order of the Discontinuous Finite Element Methods for First Order Hyperbolic Systems}, journal = {Journal of Computational Mathematics}, year = {2008}, volume = {26}, number = {5}, pages = {689--701}, abstract = {

In this paper, a discontinuous finite element method for the positive and symmetric, first-order hyperbolic systems (steady and nonsteady state) is constructed and analyzed by using linear triangle elements, and the $O(h^2)$-order optimal error estimates are derived under the assumption of strongly regular triangulation and the $H^3$-regularity for the exact solutions. The convergence analysis is based on some superclose estimates of the interpolation approximation. Finally, we discuss the Maxwell equations in a two-dimensional domain, and numerical experiments are given to validate the theoretical results.

}, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/8652.html} }