A posteriori error analysis for a cut cell finite volume method

We describe a hybrid modeling-discretization numerical method for approximating the solution of an elliptic problem with a discontinuous diffusion coefficient that is suited for cut-cell problems in which the discontinuity interface is not resolved by the mesh. The method is inspired by the well-known Ghost Fluid Method. We carry out an a posteriori error analysis for the numerical solution for the error in a quantity of interest that is based on variational analysis, residual error and the adjoint problem. We separately identify the effects of discretization, modeling and quadrature errors on the error in the quantity of interest. We illustrate the properties of the method and the estimate in a series of examples.