Numerical approximation of PDE system fixed-point maps via Newton's method
DOI10.1016/0377-0427(91)90172-GzbMath0760.65111OpenAlexW2019253783MaRDI QIDQ1184124
Publication date: 28 June 1992
Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/0377-0427(91)90172-g
finite elementsNewton methodDirichlet boundary value problemweakly nonlinear systemtwo-sided estimationfixed-point mapKrasnosel'skii method
Nonlinear boundary value problems for linear elliptic equations (35J65) Error bounds for boundary value problems involving PDEs (65N15) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Applications to the sciences (65Z05)
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Cites Work
- L\({}_{\infty}\) stability of finite element approximations to elliptic gradient equations
- An adaptive Newton algorithm based on numerical inversion: Regularization as postconditioner
- Approximate Newton methods and homotopy for stationary operator equations
- Newton's method for gradient equations based upon the fixed point map: Convergence and complexity study
- Approximation of nonlinear evolution systems
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- Consistency of Semiconductor Modeling: An Existence/Stability Analysis for the Stationary Van Roosbroeck System
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