Volume 5, Issue 4
An $L^∞$-Error Estimate for the $h$-$p$ Version Continuous Petrov-Galerkin Method for Nonlinear Initial Value Problems

Lijun Yi

East Asian J. Appl. Math., 5 (2015), pp. 301-311.

Published online: 2018-02

Export citation
  • Abstract

The $h$-$p$ version of the continuous Petrov-Galerkin time stepping method is analyzed for nonlinear initial value problems. An $L^∞$-error bound explicit with respect to the local discretization and regularity parameters is derived. Numerical examples are provided to illustrate the theoretical results.

  • Keywords

Initial value problems, $h-p$ version, time stepping method, continuous Petrov-Galerkin method, error bound.

  • AMS Subject Headings

65L60, 65L05, 65L70

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address
  • BibTex
  • RIS
  • TXT
@Article{EAJAM-5-301, author = {}, title = {An $L^∞$-Error Estimate for the $h$-$p$ Version Continuous Petrov-Galerkin Method for Nonlinear Initial Value Problems}, journal = {East Asian Journal on Applied Mathematics}, year = {2018}, volume = {5}, number = {4}, pages = {301--311}, abstract = {

The $h$-$p$ version of the continuous Petrov-Galerkin time stepping method is analyzed for nonlinear initial value problems. An $L^∞$-error bound explicit with respect to the local discretization and regularity parameters is derived. Numerical examples are provided to illustrate the theoretical results.

}, issn = {2079-7370}, doi = {https://doi.org/10.4208/eajam.310315.070815a}, url = {http://global-sci.org/intro/article_detail/eajam/10814.html} }
TY - JOUR T1 - An $L^∞$-Error Estimate for the $h$-$p$ Version Continuous Petrov-Galerkin Method for Nonlinear Initial Value Problems JO - East Asian Journal on Applied Mathematics VL - 4 SP - 301 EP - 311 PY - 2018 DA - 2018/02 SN - 5 DO - http://doi.org/10.4208/eajam.310315.070815a UR - https://global-sci.org/intro/article_detail/eajam/10814.html KW - Initial value problems, $h-p$ version, time stepping method, continuous Petrov-Galerkin method, error bound. AB -

The $h$-$p$ version of the continuous Petrov-Galerkin time stepping method is analyzed for nonlinear initial value problems. An $L^∞$-error bound explicit with respect to the local discretization and regularity parameters is derived. Numerical examples are provided to illustrate the theoretical results.

Lijun Yi. (1970). An $L^∞$-Error Estimate for the $h$-$p$ Version Continuous Petrov-Galerkin Method for Nonlinear Initial Value Problems. East Asian Journal on Applied Mathematics. 5 (4). 301-311. doi:10.4208/eajam.310315.070815a
Copy to clipboard
The citation has been copied to your clipboard