Optimality of adaptive Galerkin methods for random parabolic partial differential equations

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:263

Article

Gittelson, Claude Jeffrey¹  Andreev, Roman²  Schwab, Christoph³ 

[1] Purdue Univ, Dept Math, W Lafayette, IN 47907 USA

[2] Austrian Acad Sci, RICAM, A-4040 Linz, Austria

[3] ETH, Seminar Appl Math, CH-8092 Zurich, Switzerland

关键词: Partial differential equations with random coefficients;    Parabolic differential equations;    Uncertainty quantification;    Stochastic finite element methods;    Adaptive methods;    Wavelets;   

DOI  :  10.1016/j.cam.2013.12.031

来源: Elsevier

【 摘 要 】

Galerkin discretizations of a class of parametric and random parabolic partial differential equations (PDEs) are considered. The parabolic PDEs are assumed to depend on a vector Y = (y(1), y(2),...) of possibly countably many parameters yi which are assumed to take values in [-1, 1]. Well-posedness of weak formulations of these parametric equations in suitable Bochner spaces is established. Adaptive Galerkin discretizations of the equation based on a tensor product of a generalized polynomial chaos in the parameter domain Gamma = [-1, 1](N), and of suitable wavelet bases in the time interval I = [0, T] and the spatial domain D c R-d are proposed and their optimality is established. (c) 2013 Elsevier B.V. All rights reserved.

【 授权许可】

Free