On the updating and assembly of the Hessian matrix in finite element methods

DOI10.1016/0045-7825(88)90095-3zbMath0673.65068OpenAlexW2020937688MaRDI QIDQ1120970

Joseph M. L. Maubach, Owe Axelsson

Publication date: 1988

Published in: Computer Methods in Applied Mechanics and Engineering (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0045-7825(88)90095-3

zbMATH Keywords

numerical examplespreconditioningfinite elementfactorizationNewton methodselectromagnetic field equationtorsion of an elastic barpotential equation in aerodynamics

Mathematics Subject Classification ID

Numerical computation of solutions to systems of equations (65H10) Nonlinear boundary value problems for linear elliptic equations (35J65) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Partial differential equations of mathematical physics and other areas of application (35Q99)

Related Items (12)

Sobolev space preconditioning for Newton's method using domain decomposition ⋮ Variable preconditioning for strongly nonlinear elliptic problems ⋮ An iterative algorithm for finite element analysis. ⋮ On the Lipschitz continuity of derivatives for some scalar nonlinearities ⋮ On the numerical performance of a sharp a posteriori error estimator for some nonlinear elliptic problems. ⋮ Discrete maximum principles for finite element solutions of nonlinear elliptic problems with mixed boundary conditions ⋮ Discrete maximum principles for finite element solutions of some mixed nonlinear elliptic problems using quadratures ⋮ Sharp upper global a posteriori error estimates for nonlinear elliptic variational problems ⋮ Equivalent operator preconditioning for elliptic problems ⋮ AN INEXACT NEWTON METHOD WITH INNER PRECONDITIONED CG FOR NON-UNIFORMLY MONOTONE ELLIPTIC PROBLEMS ⋮ Constant wavefront iteration methods for nine- and 15-point difference matrices ⋮ Preconditioning operators and Sobolev gradients for nonlinear elliptic problems

Cites Work

• On the numerical solution of nonlinear problems in fluid dynamics by least squares and finite element methods. II: Application to transonic flow simulations
• Some integration formulas for a four-node isoparametric element
• Multiple grid and Osher's scheme for the efficient solution of the steady Euler equations
• The natural factor formulation of the stiffness for the matrix displacement method
• Cubature formulas of degree eleven for symmetric planar regions
• Iterative methods for the solution of the Navier equations of elasticity
• On algebraic multilevel preconditioning methods
• High degree efficient symmetrical Gaussian quadrature rules for the triangle
• Inexact Newton Methods
• Three dimensional analysis of compressible potential flows with the finite element method
• The Convergence of an Algorithm for Solving Sparse Nonlinear Systems
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