A nonconforming a posteriori estimator for the coupling of cell-centered finite volume and boundary element methods

Abstract

The coupling of the cell-centered finite volume method and the boundary element method is an interesting approach to solve elliptic problems on an unbounded domain, where local flux conservation is important. Based on the piecewise constant interior finite volume solution we define a Morley-type interpolant built on a nonconforming finite element. Together with the Cauchy data of the exterior boundary element solution this allows us to define a residual-based a posteriori error estimator. With respect to an energy norm we prove reliability and efficiency of this estimator and use its local contributions to steer an adaptive mesh-refining algorithm. In two examples we illustrate the effectiveness of the new adaptive coupling method and compare it with the coupling approach with a conforming Morley interpolant.Mathematics Subject Classification 65N08 · 65N38 · 65N15 · 65N50 · 76M12 · 76M15