An adaptive wavelet method and its analysis for parabolic equations
Qiang Guo, Dong Liang · Numerical Algebra Control and Optimization · 2013
In this paper, we analyze an adaptive wavelet method with variabletime step sizes and space refinement for parabolic equations. Theadvantages of multi-resolution wavelet processes combined withcertain equivalences involving weighted sequence norms of waveletcoefficients allow us to set up an efficient adaptive algorithmproducing locally refined spaces for each time step. Reliable andefficient a posteriori error estimate is derived, which assesses thediscretization error with respect to a given quantity of physicalinterest. The influence of the time and space discretization errorsis separated into different error indicators. We prove that theproposed adaptive wavelet algorithm terminates in a finite number ofiterations for any given accuracy.