Adaptive vertex-centered finite volume methods for general second-order linear elliptic PDEs
Provides theoretical convergence guarantees for adaptive finite volume methods on a broader class of PDEs, benefiting numerical analysts and practitioners solving convection-diffusion problems.
The paper proves optimal convergence rates for adaptive vertex-centered finite volume methods applied to general second-order linear elliptic PDEs, extending prior work from symmetric to non-symmetric problems including convection.
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.