Contributions to Books:
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,
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
Electronic version of the publication:
Created from the Publication Database of the Vienna University of Technology.