ON THE CONVERGENCE OF ADAPTIVE STOCHASTIC COLLOCATION FOR ELLIPTIC PARTIAL DIFFERENTIAL EQUATIONS WITH AFFINE DIFFUSION
SIAM JOURNAL ON NUMERICAL ANALYSIS(2022)
摘要
Convergence of an adaptive collocation method for the parametric stationary diffusion equation with finite-dimensional affine coefficient is shown. The adaptive algorithm relies on a recently introduced residual-based reliable a posteriori error estimator. For the convergence proof, a strategy recently used for a stochastic Galerkin method with a hierarchical error estimator is transferred to the collocation setting. Extensions to other variants of adaptive collocation methods (including the now classical approach proposed in [T. Gerstner and M. Griebel, Computing, 71 (2003), pp. 65-87]) are explored.
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关键词
random PDEs, parametric PDEs, sparse grids, stochastic collocation, highdimensional approximation, high-dimensional interpolation, adaptive algorithms
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