Error Control in Multi-Element Generalized Polynomial Chaos Method for Elliptic Problems with Random Coefficients

Error Control in Multi-Element Generalized Polynomial Chaos Method for Elliptic Problems with Random Coefficients

Year:    2009

Communications in Computational Physics, Vol. 5 (2009), Iss. 2-4 : pp. 793–820

Abstract

We develop the theory for a robust and efficient adaptive multi-element generalized polynomial chaos (ME-gPC) method for elliptic equations with random coefficients for a moderate number (O(10)) of random dimensions. We employ low-order (p ≤ 3) polynomial chaos and refine the solution using adaptivity in the parametric space. We first study the approximation error of ME-gPC and prove its hp-convergence. We subsequently generate local and global a posteriori error estimators. In order to resolve the error equations efficiently, we construct a reduced space using much smaller number of terms in the enhanced polynomial chaos space to capture the errors of ME-gPC approximation. Based on the a posteriori estimators, we propose and implement an adaptive ME-gPC algorithm for elliptic problems with random coefficients. Numerical results for convergence and efficiency are also presented.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/2009-CiCP-7764

Communications in Computational Physics, Vol. 5 (2009), Iss. 2-4 : pp. 793–820

Published online:    2009-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    28

Keywords: