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C. Erath, D. Praetorius:
"Adaptive vertex-centered finite volume methods for general second-order linear elliptic PDEs";
IMA J. Numer. Anal., 39 (2019), S. 983 - 1008.

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://dx.doi.org/10.1093/imanum/dry006