Application of the Mesh Independence Principle to Mesh Refinement Strategies

Application of the Mesh Independence Principle to Mesh Refinement Strategies

The Mesh Independence Principle (MIP) for a Newton iteration applied to an operator equation and its discretization for different "stepsizes" h states for a fixed starting point the number of iterations of Newton's method to obtain a fixed tolerance is eventually independent of h. Thi...

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Veröffentlicht in:SIAM journal on numerical analysis 1987-12, Vol.24 (6), p.1335-1351
Hauptverfasser: Allgower, E. L., Bohmer, K.
Format: Artikel
Sprache:eng
Schlagworte:
Algorithms
Applied mathematics
Approximation
Boundary value problems
Differential equations
Efficient strategies
Exact sciences and technology
Grid refinement
Integral equations
Iterative solutions
Mathematics
Methods
Newtons method
Nonlinear algebraic and transcendental equations
Numerical analysis
Numerical analysis. Scientific computation
Ordinary differential equations
Political independence
Sciences and techniques of general use
Textual collocation
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Beschreibung
Zusammenfassung:The Mesh Independence Principle (MIP) for a Newton iteration applied to an operator equation and its discretization for different "stepsizes" h states for a fixed starting point the number of iterations of Newton's method to obtain a fixed tolerance is eventually independent of h. This MIP is used to formulate an efficient strategy for the solution of nonlinear equations amounting to the work equivalent of two or three Newton iterates for the smallest h. Examples are given.
ISSN:0036-1429
1095-7170
DOI:10.1137/0724086