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

被引：2

作者：

Li, Meng ^{[1
]}

Luo, Xianbing ^{[1
]}

机构：

[1] Guizhou Univ, Sch Math & Stat, Guiyang 550025, Peoples R China

来源：

MATHEMATICS | 2021年 / 9卷 / 09期

关键词：

elliptic PDEs; random coefficients; hybridizable discontinuous Galerkin; multilevel Monte Carlo; PARTIAL-DIFFERENTIAL-EQUATIONS; ERROR ANALYSIS; GALERKIN; APPROXIMATIONS;

D O I：

10.3390/math9091072

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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(w, 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.

引用

页数：13

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