A POSTERIORI ERROR ESTIMATE AND ADAPTIVE MESH REFINEMENT FOR THE CELL-CENTERED FINITE VOLUME METHOD FOR ELLIPTIC BOUNDARY VALUE PROBLEMS

摘要

We extend a result of Nicaise [SIAM J. Numer. Anal., 43 (2005), pp. 1481–1503] for the a posteriori error estimation of the cell-centered finite volume method for the numerical solution of elliptic problems. Having computed the piecewise constant finite volume solution uh, we compute a Morley-type interpolant Iuh. For the exact solution u, the energy error T (u Iuh)L2 can be controlled efficiently and reliably by a residual-based a posteriori error estimator η. The local contributions of η are used to steer an adaptive mesh-refining algorithm. A model example serves the Laplace equation in two dimensions with mixed Dirichlet–Neumann boundary conditions.