Asymptotic Mesh Independence of Newton's Method Revisited
Zitieren Sie bitte immer diese URN: urn:nbn:de:0297-zib-7352
- The paper presents a new affine invariant theory on asymptotic mesh independence of Newton's method in nonlinear PDEs. Compared to earlier attempts, the new approach is both much simpler and more natural from the algorithmic point of view. The theory is exemplified at collocation methods for ODE boundary value problems and at finite element methods for elliptic PDE problems.
Verfasserangaben: | Martin WeiserORCiD, Anton Schiela, Peter Deuflhard |
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Dokumentart: | ZIB-Report |
Freies Schlagwort / Tag: | Newton method; collocation method; finite element method; mesh independence; nonlinear partial differential equations |
MSC-Klassifikation: | 65-XX NUMERICAL ANALYSIS / 65Jxx Numerical analysis in abstract spaces / 65J15 Equations with nonlinear operators (do not use 65Hxx) |
65-XX NUMERICAL ANALYSIS / 65Nxx Partial differential equations, boundary value problems / 65N22 Solution of discretized equations [See also 65Fxx, 65Hxx] | |
65-XX NUMERICAL ANALYSIS / 65Nxx Partial differential equations, boundary value problems / 65N30 Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods | |
Datum der Erstveröffentlichung: | 12.05.2003 |
Schriftenreihe (Bandnummer): | ZIB-Report (03-13) |
ZIB-Reportnummer: | 03-13 |
Verlagspublikation: | Appeared in: SIAM Journal on Numerical Analysis Vol. 42, No. 5, pp. 1830-1845 |