A Regularized Newton-Like Method for Nonlinear PDE

DOI10.1080/01630563.2015.1069328zbMath1342.65220arXiv1412.6487OpenAlexW1921185783WikidataQ59394147 ScholiaQ59394147MaRDI QIDQ2795101

Sara Pollock

Publication date: 18 March 2016

Published in: Numerical Functional Analysis and Optimization (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1412.6487

zbMATH Keywords

convergencenumerical examplefinite elementadaptive methodsNewton-like methodnonlinear elliptic problemTikhonov regularizationmesh refinement

Mathematics Subject Classification ID

Nonlinear elliptic equations (35J60) Stability and convergence of numerical methods for boundary value problems involving PDEs (65N12) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs (65N50) Numerical solution of discretized equations for boundary value problems involving PDEs (65N22) Numerical methods for ill-posed problems for boundary value problems involving PDEs (65N20)

Related Items (4)

Uniqueness of discrete solutions of nonmonotone PDEs without a globally fine mesh condition ⋮ Pseudo-transient ghost fluid methods for the Poisson-Boltzmann equation with a two-component regularization ⋮ An Improved Method for Solving Quasi-linear Convection Diffusion Problems on a Coarse Mesh ⋮ Stabilized and inexact adaptive methods for capturing internal layers in quasilinear PDE

Cites Work

• On the solution of nonlinear two-point boundary value problems on successively refined grids
• Global approximate Newton methods
• Adaptive Inexact Newton Methods with A Posteriori Stopping Criteria for Nonlinear Diffusion PDEs
• Newton Methods for Nonlinear Problems
• Parameter choice in Banach space regularization under variational inequalities
• Convergence rates for Tikhonov regularisation of non-linear ill-posed problems
• A convergence analysis of the iteratively regularized Gauss–Newton method under the Lipschitz condition
• Morozov's discrepancy principle and Tikhonov-type functionals
• Parameter Selection for Newton-Like Methods Applicable to Nonlinear Partial Differential Equations
• Optimal a Posteriori Parameter Choice for Tikhonov Regularization for Solving Nonlinear Ill-Posed Problems
• Some Newton-type methods for the regularization of nonlinear ill-posed problems
• Convergence Analysis of Pseudo-Transient Continuation
• Pseudotransient Continuation and Differential-Algebraic Equations
• Two-Grid Discretization Techniques for Linear and Nonlinear PDE<scp>s</scp>
• The Mathematical Theory of Finite Element Methods
• Pseudo-Transient Continuation for Nonsmooth Nonlinear Equations
• Adaptive numerical treatment of elliptic systems on manifolds

This page was built for publication: A Regularized Newton-Like Method for Nonlinear PDE