Error Control in Multi-Element Generalized Polynomial ChaosMethod for Elliptic Problemswith Random Coefficients

نویسندگان

  • Xiaoliang Wan
  • George Em Karniadakis
چکیده

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 loworder (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 hpconvergence. 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. AMS subject classifications: 65C20, 65C30

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تاریخ انتشار 2008