Partial Differential Equations [chapter]

2005 Applied Numerical Methods Using MATLAB®  
We study the Besov regularity as well as linear and nonlinear approximation of random functions on bounded Lipschitz domains in R d . The random functions are given either (i) explicitly in terms of a wavelet expansion or (ii) as the solution of a Poisson equation with a right-hand side in terms of a wavelet expansion. In the case (ii) we derive an adaptive wavelet algorithm that achieves the nonlinear approximation rate at a computational cost that is proportional to the degrees of freedom.
more » ... rees of freedom. These results are matched by computational experiments. Mathematics Subject Classification (2010). 60H35, 65C30, 65T60, 41A25, Secondary: 41A63.
doi:10.1002/0471705195.ch9 fatcat:6wc55sxp6jb27mbv3r53aztxpq