Computable error estimates for Monte Carlo finite element approximation of elliptic PDE with lognormal diffusion coefficients

Abstract
The Monte Carlo (and Multi-level Monte Carlo) finite element method can be used to approximate observables of solutions to diffusion equations with lognormal distributed diffusion coefficients, e.g. modeling ground water flow. Typical models use lognormal diffusion coefficients with H´ older regularity of order up to 1/2 a.s. This low regularity implies that the high frequency finite element approximation error (i.e. the error from frequencies larger than the mesh frequency) is not negligible and can be larger than the computable low frequency error. We address how the total error can be estimated by the computable error.

Conference/Event Name
Advances in Uncertainty Quantification Methods, Algorithms and Applications (UQAW 2016)

Permanent link to this record