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C. Erath, D. Praetorius:
"Adaptive vertex-centered finite volume methods for general second-order linear elliptic PDEs";
in: "ASC Report 17/2017", issued by: Institute for Analysis and Scientific Computing; Vienna University of Technology, Wien, 2017, ISBN: 978-3-902627-10-0, 1 - 20.

We prove optimal convergence rates for the discretization of a general second-order linear elliptic PDE with an adaptive vertex-centered finite volume scheme. While our prior work Erath and Praetorius [SIAM J. Numer. Anal., 54 (2016), pp. 2228-2255] was restricted to symmetric problems, the present analysis also covers non-symmetric problems and hence the important case of present convection.

finite volume method, Céa-type quasi-optimality, a posteriori error estimator,finite volume method, Céa-type quasi-optimality, a posteriori error estimators,finite volume method, Céa-type quasi-optimality, a posteriori error estimators,

http://www.asc.tuwien.ac.at/preprint/2017/asc17x2017.pdf