An ensemble Monte Carlo HDG method for parabolic PDEs with random coefficients

Abstract

We use Monte Carlo, ensemble and hybrid discontinuous Galerkin method (EMC-HDG) to numerically solve parabolic partial differential equations (PDEs) with random coefficients. The proposed method reduces the computational cost and the storage requirement by solving multiple linear systems with a common coefficient matrix. Error analysis shows the proposed method is first-order accurate in time and optimal $L^2$ convergence order in physical space. In the end, several numerical experiments are presented to verify the theoretical results.

Keywords:

• Parabolic PDEs
• random coefficients
• HDG method
• ensemble
• Monte Carlo

2010 AMS SUBJECT CLASSIFICATIONS:

• 35R60
• 60H35
• 65C05
• 65M15
• 65M60

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

We are particularly grateful to the National Natural Science Foundation of China (NSF of China) for its support [grant number 11961008].