Convergence Analysis and Cost Estimate of an MLMC-HDG Method for Elliptic PDEs with Random Coefficients

Meng Li and Xianbing Luo
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Meng Li: School of Mathematics and Statistics, Guizhou University, Guiyang 550025, China
Xianbing Luo: School of Mathematics and Statistics, Guizhou University, Guiyang 550025, China

Mathematics, 2021, vol. 9, issue 9, 1-13

Abstract: We considered an hybridizable discontinuous Galerkin (HDG) method for discrete elliptic PDEs with random coefficients. By an approach of projection, we obtained the error analysis under the assumption that a ( ? , x ) is uniformly bounded. Together with the HDG method, we applied a multilevel Monte Carlo (MLMC) method (MLMC-HDG method) to simulate the random elliptic PDEs. We derived the overall convergence rate and total computation cost estimate. Finally, some numerical experiments are presented to confirm the theoretical results.

Keywords: elliptic PDEs; random coefficients; hybridizable discontinuous Galerkin; multilevel Monte Carlo (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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