Adaptive Cell-Centered Finite Volume Method

In our talk, we propose an adaptive mesh-refining strategy for the cell-centered FVM based on some a posteriori error control for the quantity ‖∇T (u − Iuh)‖L2 . Here, uh ∈ P (T ) denotes the FVM approximation of u and I is a certain interpolation operator. As model example serves the Laplace equation with mixed boundary conditions, where our contributions extend a result of [NIC05]. Moreover, this approach allows the coupling of finite volume schemes with the boundary element method, which is a new and fruitful combination of the shown ideas in [CAR99a, CAR99b] and given below.