We discuss the application of multilevel Monte Carlo methods to elliptic partial differential equations with random coefficients. Such problems arise, for example, in uncertainty quantification in subsurface flow modeling. We give a brief review of recent advances in the numerical analysis of the multilevel algorithm under minimal assumptions on the random coefficient, and extend the analysis to cover also tensor-valued coefficients, as well as point evaluations. Our analysis includes as an example log-normal random coefficients, which are frequently used in applications.
|Title of host publication||Proceedings - Winter Simulation Conference|
|Publication status||Published - 2012|
|Event||2012 Winter Simulation Conference, WSC 2012 - Berlin, Germany|
Duration: 9 Dec 2012 → 12 Dec 2012
|Conference||2012 Winter Simulation Conference, WSC 2012|
|Period||9/12/12 → 12/12/12|