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Volume 19, Issue 4
Improved Error Estimates for Mixed Finite Element for Nonlinear Hyperbolic Equations: The Continuous-Time Case

Yan-Ping Chen & Yuan-Qing Huang

J. Comp. Math., 19 (2001), pp. 385-392.

Published online: 2001-08

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  • Abstract

Improved $L_2$-error estimates are computed for mixed finite element methods for second order nonlinear hyperbolic equations. Results are given for the continuous-time case. The convergence of the values for both the scalar function and the flux is demonstrated. The technique used here covers the lowest-order Raviart-Thomas spaces, as well as the higher-order spaces. A second paper will present the analysis of a fully discrete scheme.

  • Keywords

Nonlinear hyperbolic equations, Mixed finite element methods, Error estimates, Superconvergence.

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  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JCM-19-385, author = {Chen , Yan-Ping and Huang , Yuan-Qing}, title = {Improved Error Estimates for Mixed Finite Element for Nonlinear Hyperbolic Equations: The Continuous-Time Case}, journal = {Journal of Computational Mathematics}, year = {2001}, volume = {19}, number = {4}, pages = {385--392}, abstract = {

Improved $L_2$-error estimates are computed for mixed finite element methods for second order nonlinear hyperbolic equations. Results are given for the continuous-time case. The convergence of the values for both the scalar function and the flux is demonstrated. The technique used here covers the lowest-order Raviart-Thomas spaces, as well as the higher-order spaces. A second paper will present the analysis of a fully discrete scheme.

}, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/8991.html} }
TY - JOUR T1 - Improved Error Estimates for Mixed Finite Element for Nonlinear Hyperbolic Equations: The Continuous-Time Case AU - Chen , Yan-Ping AU - Huang , Yuan-Qing JO - Journal of Computational Mathematics VL - 4 SP - 385 EP - 392 PY - 2001 DA - 2001/08 SN - 19 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/8991.html KW - Nonlinear hyperbolic equations, Mixed finite element methods, Error estimates, Superconvergence. AB -

Improved $L_2$-error estimates are computed for mixed finite element methods for second order nonlinear hyperbolic equations. Results are given for the continuous-time case. The convergence of the values for both the scalar function and the flux is demonstrated. The technique used here covers the lowest-order Raviart-Thomas spaces, as well as the higher-order spaces. A second paper will present the analysis of a fully discrete scheme.

Chen , Yan-Ping and Huang , Yuan-Qing. (2001). Improved Error Estimates for Mixed Finite Element for Nonlinear Hyperbolic Equations: The Continuous-Time Case. Journal of Computational Mathematics. 19 (4). 385-392. doi:
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