On finite element schemes of the dirichlet problem

DOI10.1080/01630568108816081zbMath0469.65071OpenAlexW2070439670MaRDI QIDQ3923542

Kazuo Ishihara

Publication date: 1981

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

Full work available at URL: https://doi.org/10.1080/01630568108816081

zbMATH Keywords

Dirichlet problemmonotone sequenceserror estimatesuniform convergencenumerical examplesfinite elementiterative methodsdiscrete maximum principlepiecewise linear polynomials

Mathematics Subject Classification ID

Numerical computation of solutions to systems of equations (65H10) 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)

Related Items (8)

Explicit iterations with monotonicity for finite element approximations applied to a system of nonlinear elliptic equations ⋮ Strong and weak discrete maximum principles for matrices associated with elliptic problems ⋮ Finite element approximations applied to the nonlinear boundary value problem \(\Delta(u)=b(u)^2\) ⋮ Projected successive overrelaxation method for finite-element solutions to the Dirichlet problem for a system of nonlinear elliptic equations ⋮ Discrete minimum and maximum principles for finite element approximations of non-monotone elliptic equations ⋮ Finite element solutions for radiation cooling problems with nonlinear boundary conditions ⋮ Monotone explicit iterations of the finite element approximations for the nonlinear boundary value problem ⋮ Explicit monotone iterations providing upper and lower bounds for finite element solution with nonlinear radiation boundary conditions

Cites Work

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• On a system of nonlinear parabolic equations arising in chemical engineering
• On the asymptotic behavior of solutions of a mildly nonlinear parabolic system
• Mildly nonlinear elliptic partial differential equations and their numerical solution. I
• Le problème de Dirichlet pour les équations elliptiques du second ordre à coefficients discontinus
• Discrete maximum principle for finite-difference operators
• On the Cauchy problem for a simple degenerate diffusion system
• Maximum principle and uniform convergence for the finite element method
• Elliptic Partial Differential Equations of Second Order
• Difference methods for a nonlinear elliptic system of partial differential equations

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