Numerical solution of parabolic equations in high dimensions
Tobias Von Petersdorff, Christoph Schwab (2004)
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
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We consider the numerical solution of diffusion problems in for and for in dimension . We use a wavelet based sparse grid space discretization with mesh-width and order , and discontinuous Galerkin time-discretization of order on a geometric sequence of many time steps. The linear systems in each time step are solved iteratively by GMRES iterations with a wavelet preconditioner. We prove that this algorithm gives an -error of for where is the total number of...