Adaptive vertex-centered finite volume methods for general second-order linear elliptic PDEs

TL;DR

This paper establishes optimal convergence rates for an adaptive vertex-centered finite volume method applied to general second-order linear elliptic PDEs, including non-symmetric cases with convection.

Contribution

It extends previous symmetric problem analysis to non-symmetric problems, covering convection in elliptic PDEs with adaptive finite volume schemes.

Findings

Proves optimal convergence rates for the scheme.

Includes non-symmetric PDEs with convection.

Builds on and generalizes prior symmetric problem results.

Abstract

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.