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 - <p style="text-align: justify;">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.</p>