Adaptive wavelet methods for the stochastic Poisson equation

作者：Cioica Petru A; Dahlke Stephan; Doehring Nicolas; Kinzel Stefan^*; Lindner Felix; Raasch Thorsten; Ritter Klaus; Schilling Rene L

来源：BIT Numerical Mathematics, 2012, 52(3): 589-614.

DOI：10.1007/s10543-011-0368-7

• Elliptic stochastic partial differential equation
• Wavelets
• Besov regularity
• Approximation rates
• Nonlinear approximation
• Adaptive methods

We study the Besov regularity as well as linear and nonlinear approximation of random functions on bounded Lipschitz domains in a%26quot;e (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. These results are matched by computational experiments.

• 出版日期2012-9