A Crank-Nicolson Petrov-Galerkin method with quadrature for semi-linear parabolic problems

We propose and analyze an application of a fully discrete C-2 spline quadrature Petrov-Galerkin method for spatial discretization of semi-linear parabolic initial-boundary value problems on rectangular domains. We prove second order in time and optimal order H-1 norm convergence in space for the extrapolated Crank-Nicolson quadrature Petrov-Galerkin scheme. We demonstrate numerically both L-2 and H-1 norm optimal order convergence of the scheme even if the nonlinear source term is not smooth. (c) 2005 Wiley Periodicals, Inc.