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

摘要

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.