Asymptotic Mesh Independence of Newton's Method Revisited

Please always quote using this 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.

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Metadaten
Author:Martin WeiserORCiD, Anton Schiela, Peter Deuflhard
Document Type:ZIB-Report
Tag:Newton method; collocation method; finite element method; mesh independence; nonlinear partial differential equations
MSC-Classification: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
Date of first Publication:2003/05/12
Series (Serial Number):ZIB-Report (03-13)
Published in:Appeared in: SIAM Journal on Numerical Analysis Vol. 42, No. 5, pp. 1830-1845