Asymptotic Mesh Independence of Newton's Method Revisited

DOI10.1137/S0036142903434047zbMath1081.65051OpenAlexW2136558717MaRDI QIDQ4653935

Peter Deuflhard, Anton Schiela, Martin Weiser

Publication date: 1 March 2005

Published in: SIAM Journal on Numerical Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/s0036142903434047

zbMATH Keywords

Newton's methodfinite element methodsnonlinear operator equationsaffine invarianceasymptotic mesh independence

Mathematics Subject Classification ID

Iterative procedures involving nonlinear operators (47J25) Nonlinear boundary value problems for linear elliptic equations (35J65) 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 solutions to equations with nonlinear operators (65J15)

Related Items (15)

Coupling vs decoupling approaches for PDE/ODE systems modeling intercellular signaling ⋮ Self-consistent solution of cosmological radiation-hydrodynamics and chemical ionization ⋮ Third-order iterative methods under Kantorovich conditions ⋮ Geodesic finite elements on simplicial grids ⋮ An improved iterative HDG approach for partial differential equations ⋮ An interior point algorithm with inexact step computation in function space for state constrained optimal control ⋮ Newton's method and a mesh-independence principle for certain semilinear boundary-value problems ⋮ Anderson acceleration and application to the three-temperature energy equations ⋮ The convergence of an interior point method for an elliptic control problem with mixed control-state constraints ⋮ Mesh-independence of semismooth Newton methods for Lavrentiev-regularized state constrained nonlinear optimal control problems ⋮ Extrapolation methods for the numerical solution of nonlinear Fredholm integral equations ⋮ Numerical Methods for Power-Law Diffusion Problems ⋮ Geodesic finite elements for Cosserat rods ⋮ Determining the optimal parameters for the MHD flow and heat transfer with variable viscosity and Hall effect ⋮ Semilocal convergence for Halley's method under weak Lipschitz condition

This page was built for publication: Asymptotic Mesh Independence of Newton's Method Revisited