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

Handle URI:
http://hdl.handle.net/10754/624869
Title:
Computable error estimates for Monte Carlo finite element approximation of elliptic PDE with lognormal diffusion coefficients
Authors:
Hall, Eric; Haakon, Hoel; Sandberg, Mattias; Szepessy, Anders; Tempone, Raul ( 0000-0003-1967-4446 )
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.
KAUST Department:
Computer, Electrical and Mathematical Sciences & Engineering (CEMSE)
Conference/Event name:
Advances in Uncertainty Quantification Methods, Algorithms and Applications (UQAW 2016)
Issue Date:
9-Jan-2016
Type:
Presentation
Appears in Collections:
Conference on Advances in Uncertainty Quantification Methods, Algorithms and Applications (UQAW 2016)

Full metadata record

DC FieldValue Language
dc.contributor.authorHall, Ericen
dc.contributor.authorHaakon, Hoelen
dc.contributor.authorSandberg, Mattiasen
dc.contributor.authorSzepessy, Andersen
dc.contributor.authorTempone, Raulen
dc.date.accessioned2017-06-08T06:32:30Z-
dc.date.available2017-06-08T06:32:30Z-
dc.date.issued2016-01-09-
dc.identifier.urihttp://hdl.handle.net/10754/624869-
dc.description.abstractThe 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.en
dc.titleComputable error estimates for Monte Carlo finite element approximation of elliptic PDE with lognormal diffusion coefficientsen
dc.typePresentationen
dc.contributor.departmentComputer, Electrical and Mathematical Sciences & Engineering (CEMSE)en
dc.conference.dateJanuary 5-10, 2016en
dc.conference.nameAdvances in Uncertainty Quantification Methods, Algorithms and Applications (UQAW 2016)en
dc.conference.locationKAUSTen
dc.contributor.institutionUniversity of Osloen
dc.contributor.institutionKTH Royal Institute of Technology in Stockholmen
dc.contributor.institutionUniversity of Massachusetts at Amhersten
kaust.authorTempone, Raulen
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