Abstract
We define the higher order moments associated to the stochastic solution of an elliptic BVP in D⊂ℝd with stochastic input data. We prove that the k-th moment solves a deterministic problem in D k⊂ℝdk, for which we discuss well-posedness and regularity. We discretize the deterministic k-th moment problem using sparse grids and, exploiting a spline wavelet basis, we propose an efficient algorithm, of logarithmic-linear complexity, for solving the resulting system.
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Supported in part under the IHP network Breaking Complexity of the EC (contract number HPRN-CT-2002-00286) with support by the Swiss Federal Office for Science and Education under grant No. BBW 02.0418.
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Schwab, C., Todor, R. Sparse Finite Elements for Stochastic Elliptic Problems – Higher Order Moments. Computing 71, 43–63 (2003). https://doi.org/10.1007/s00607-003-0024-4
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DOI: https://doi.org/10.1007/s00607-003-0024-4