Abstract
In this work, we investigate a novel two-level discretization method for the elliptic equations with random input data. Motivated by the two-grid method for deterministic nonlinear partial differential equations introduced by Xu [36], our two-level discretization method uses a two-grid finite element method in the physical space and a two-scale stochastic collocation method with sparse grid in the random domain. Specifically, we solve a semilinear equations on a coarse mesh
Funding statement: Luoping Chen is supported by the National Natural Science Foundation of China (No. 11501473) and the Fundamental Research Funds for the Central Universities of China (No. 2682016CX108). Yanping Chen is supported National Natural Science Foundation of China (No. 11671157 and No. 91430104). Xiong Liu is supported by Lingnan Normal University general project (No. 2014YL1408).
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