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International Journal for Uncertainty Quantification
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ISSN Imprimer: 2152-5080
ISSN En ligne: 2152-5099

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International Journal for Uncertainty Quantification

DOI: 10.1615/Int.J.UncertaintyQuantification.2015012533
pages 415-432

A POSTERIORI ERROR ESTIMATION FOR A CUT CELL FINITE VOLUME METHOD WITH UNCERTAIN INTERFACE LOCATION

J. B. Collins
Department of Mathematics, Chemistry, and Physics, West Texas A&M University, Canyon, Texas 79016, USA
Donald Estep
Department of Statistics, Colorado State University, Fort Collins, Colorado 80523-1877, USA
Simon Tavener
Department of Mathematics, Colorado State University, Fort Collins, Colorado 80523, USA

RÉSUMÉ

We study a simple diffusive process in which the diffusivity is discontinuous across an interface interior to the domain. In many situations, the location of the interface is measured at a small number of locations and these measurements contain error. Thus the location of the interface and the solution itself are subject to uncertainty. Further, the location of the interface may have a strong impact on the accuracy of the solution. A Monte Carlo approach is employed which requires solving a large number of sample problems, each with a different interface location. To solve these problems, a mixed finite element cut-cell method has been developed that does not require the mesh to conform to the interface. An efficient adjoint-based a posteriori technique is used to estimate the error in a quantity of interest for each sample problem. This error has a component due to the numerical approximation of the diffusive process and a component arising from the uncertainty in the interface location. A recognition of these separate sources of error is necessary in order to construct effective adaptivity strategies.


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