Volume 23, Issue 3
The Optimal Order Error Estimates for Finite Element Approximations to Hyperbolic Problems

Tie Zhang

DOI:

J. Comp. Math., 23 (2005), pp. 275-284

Published online: 2005-06

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  • Abstract

In this paper, the linear finite element approximation to the positive and symmetric, linear hyperbolic systems is analyzed and an $O(h^2)$ order error estimate is established under the conditions of strongly regular triangulation and the $H^3$-regularity for the exact solutions. The convergence analysis is based on some superclose estimates derived in this paper. Our method and result here are also applicable to general hyperbolic problems. Finally, we discuss the linearized shallow water system of equations.

  • Keywords

Hyperbolic problems Finite element approximations Optimal error estimates

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@Article{JCM-23-275, author = {}, title = {The Optimal Order Error Estimates for Finite Element Approximations to Hyperbolic Problems}, journal = {Journal of Computational Mathematics}, year = {2005}, volume = {23}, number = {3}, pages = {275--284}, abstract = { In this paper, the linear finite element approximation to the positive and symmetric, linear hyperbolic systems is analyzed and an $O(h^2)$ order error estimate is established under the conditions of strongly regular triangulation and the $H^3$-regularity for the exact solutions. The convergence analysis is based on some superclose estimates derived in this paper. Our method and result here are also applicable to general hyperbolic problems. Finally, we discuss the linearized shallow water system of equations. }, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/8815.html} }
TY - JOUR T1 - The Optimal Order Error Estimates for Finite Element Approximations to Hyperbolic Problems JO - Journal of Computational Mathematics VL - 3 SP - 275 EP - 284 PY - 2005 DA - 2005/06 SN - 23 DO - http://dor.org/ UR - https://global-sci.org/intro/jcm/8815.html KW - Hyperbolic problems KW - Finite element approximations KW - Optimal error estimates AB - In this paper, the linear finite element approximation to the positive and symmetric, linear hyperbolic systems is analyzed and an $O(h^2)$ order error estimate is established under the conditions of strongly regular triangulation and the $H^3$-regularity for the exact solutions. The convergence analysis is based on some superclose estimates derived in this paper. Our method and result here are also applicable to general hyperbolic problems. Finally, we discuss the linearized shallow water system of equations.
Tie Zhang. (1970). The Optimal Order Error Estimates for Finite Element Approximations to Hyperbolic Problems. Journal of Computational Mathematics. 23 (3). 275-284. doi:
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