Error Estimates for a Mixed Hybridized Finite Volume Method for 2nd Order Elliptic Problems

In this article, we carry out the convergence analysis of the dual–mixed hybridized finite volume scheme proposed in (Marco Brera et al., Comput. Methods Appl. Mech. Eng., in press, 2010) for the numerical approximation of transport problems in symmetrizable form. Using the results of (Micheletti et al., SIAM J. Sci. Comput., 23-1:245–270, 2001; Brezzi et al., Discretization of semiconductor device problems (i), Elsevier North-Holland, Amsterdam, 2005) optimal error estimates are obtained for the scalar unknown and the flux in the appropriate graph norm, while using the techniques and analysis of (Arnold and Brezzi, Math. Modeling Numer. Anal., 19-1:7–32, 1985; Brezzi and Fortin, Mixed and Hybrid Finite Element Methods, Springer, New York, 1991) the superconvergence of the hybrid variable and of its post-processed (nonconforming) reconstruction are proved. Numerical experiments are included to support the theoretical conclusions.