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

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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.
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DOI

10.4208/eajam.310315.070815a