Abstract
For a general second order linear elliptic PDE, we show a generalized Céa 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.
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Erath, C., Praetorius, D. (2017). Céa-Type Quasi-Optimality and Convergence Rates for (Adaptive) Vertex-Centered FVM. In: Cancès, C., Omnes, P. (eds) Finite Volumes for Complex Applications VIII - Methods and Theoretical Aspects . FVCA 2017. Springer Proceedings in Mathematics & Statistics, vol 199. Springer, Cham. https://doi.org/10.1007/978-3-319-57397-7_14
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DOI: https://doi.org/10.1007/978-3-319-57397-7_14
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Online ISBN: 978-3-319-57397-7
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