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

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.