Abstract
The FDM considered in the following is to be understood as an “exterior approximation” of the BVP Au = F in the space Rn, \(n: = \left| {\bar \omega } \right|]\), where n tends to infinity as h → 0. The FDSs Ahy = Fh, with Ah ∈ L(Rn, Rn)(family of spaces of linear operators from Rn into Rn) and Fh, y ∈ Rn, are derived by approximating the BVP Au = F under the assumptions \(\text{V(}\bar \Omega \text{)}\), V(A, F) and V(u) from Section 2.1. Then, the properties of the difference operator Ah, a priori estimates and the convergence y → u as h → 0 are studied in the Rn, \(\,\text{n = n(h): = }\left| {\bar \omega } \right|\). This discussion is partially based on some papers of the author, cf. HEINRICH [5,6,7,8,9,10].
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© 1987 Akademie Verlag Berlin
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Heinrich, B. (1987). Construction of Finite Difference Approximations. In: Finite Difference Methods on Irregular Networks. International Series of Numerical Mathematics / Internationale Schriftenreihe zur Numerischen Mathematik / Série internationale d’Analyse numérique, vol 82. Birkhäuser Basel. https://doi.org/10.1007/978-3-0348-7196-9_3
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DOI: https://doi.org/10.1007/978-3-0348-7196-9_3
Publisher Name: Birkhäuser Basel
Print ISBN: 978-3-0348-7198-3
Online ISBN: 978-3-0348-7196-9
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