PDE seminar by Dr. Eric Joseph Hall (KTH, Royal Institute of Technology)

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

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 Hölder
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.

Tags: PDE, random input, error estimation, Monte Carlo metods
Published May 26, 2015 8:05 PM - Last modified May 26, 2015 8:05 PM