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Weiser, Martin ; Schiela, Anton ; Deuflhard, Peter:
Asymptotic mesh independence of Newton's method revisited.
In: SIAM Journal on Numerical Analysis.
Bd. 42
(2005)
Heft 5
.
- S. 1830-1845.
ISSN 1095-7170
DOI: https://doi.org/10.1137/S0036142903434047
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Offizieller Projekttitel Projekt-ID FZT 86: Matheon - Mathematik für Schlüsseltechnologien: Modellierung, Simulation und Optimierung realer Prozesse 5485610 |
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Deutsche Forschungsgemeinschaft |
Abstract
The paper presents a new affine invariant theory on asymptotic mesh independence of Newton's method for discretized nonlinear operator equations. Compared to earlier attempts, the new approach is both much simpler and more intuitive from the algorithmic point of view. The theory is exemplified at finite element methods for elliptic PDE problems.