A Posteriori Error Estimates for Mixed Finite Element and Finite Volume Methods for Parabolic Problems Coupled through a Boundary

Abstract

We examine two discretization schemes for solving a pair of parabolic problems with significantly different spatial and temporal scales that are coupled through a common interface: a mixed finite element method which uses a rigorous mortar element technique in both space and time for coupling and a finite volume method which employs popular ad hoc projections for coupling. We derive a posteriori error estimates to quantify the distinct sources of error for both methods as well as discuss implementation of the estimates. The estimates include expressions that quantify the effects of using a finite number of iterations when solving the discrete equations yielding the approximations. We use the estimates to investigate the consequences of particular discretization choices on the accuracy of the computations.