A posteriori error estimates and adaptive mesh refinement for the coupling of the finite volume method and the boundary element method (Q2845612)

The author extends his previous analysis on a coupling of the finite volume method and the boundary element method. He considers some 2D and 3D boundary value problems attached to divergence form linear elliptic equations formulated in an interior domain and to the Laplacian in the exterior of this domain (the complementary part). The author introduces some error estimators and then proves an a posteriori result with respect to them for the discrete system with upwinding. Thus he obtains upper and lower bounds which measure the error between the exact and the numerical solution in an energy norm. Three numerical experiments in 2D are carried out in order to validate the estimator when problems which exhibit singularities or boundary/interior layers are considered.