Adaptive vertex-centered finite volume methods for general second-order linear elliptic partial differential equations.

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