[Back]

C. Erath, D. Praetorius:
"Céa-type quasi-optimality and convergence rates for (adaptive) vertex-centered FVM";
in: "ASC Report 01/2017", issued by: Institute for Analysis and Scientific Computing; Vienna University of Technology, Wien, 2017, ISBN: 978-3-902627-10-0, 1 - 8.

For a general second order linear elliptic PDE, we show a generalized Cea lemma for a vertex-centered finite volume method (FVM). The latter implies, in particular, a comparison result between the solutions of FVM and the finite element method (FEM). Furthermore, for a symmetric PDE, i.e., no convection is present, we prove linear convergence with generically optimal algebraic rates for an adaptive FVM algorithm.

finite volume method, C´ea-type quasi-optimality, a posteriori error es-timators, adaptive algorithm, local mesh-refinement, optimal convergence rates

http://www.asc.tuwien.ac.at/preprint/2017/asc01x2017.pdf