05607598

j

05607598 Mehra, Mani Rathish Kumar, B.V. Error estimates for linear PDEs solved by wavelet based Taylor-Galerkin schemes. Int. J. Wavelets Multiresolut. Inf. Process. 7, No. 2, 143-162 (2009). 2009 World Scientific, Singapore EN wavelets time accurate schemes time adaptivity space adaptivity error estimates Zbl 1071.65133 Zbl 1089.65097

doi:10.1142/S0219691309002799

Summary: In this paper, we develop a priori and a posteriori error estimates for wavelet-Taylor-Galerkin schemes introduced in {\it M. Mehra} and {\it B. V. Rathish Kumar} [Comm. Numer. Methods Eng. 21, No. 6, 313--326 (2005; Zbl 1071.65133] and {\it B. V. Rathish Kumar} and {\it M. Mehra} [Numer. Methods Partial Differ. Equations 22, No. 2, 274--295 (2006; Zbl 1089.65097)] (particularly wavelet Taylor-Galerkin scheme based on Crank-Nicolson time stepping). We proceed in two steps. In the first step, we construct the priori estimates for the fully discrete problem. In the second step, we construct error indicators for posteriori estimates with respect to both time and space approximations in order to use adaptive time steps and wavelet adaptivity. The space error indicator is computed using the equivalent norm expressed in terms of wavelet coefficients.