TY - JOUR
T1 - The Optimal Convergence Order of the Discontinuous Finite Element Methods for First Order Hyperbolic Systems
AU - Tie Zhang, Datao Shi & Zhen Li
JO - Journal of Computational Mathematics
VL - 5
SP - 689
EP - 701
PY - 2008
DA - 2008/10
SN - 26
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/jcm/8652.html
KW - First order hyperbolic systems, Discontinuous finite element method, Convergence order estimate.
AB - <p style="text-align: justify;">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.</p>