Finite element approximations applied to the nonlinear boundary value problem \(\Delta(u)=b(u)^2\)

DOI10.2977/prims/1195184014zbMath0492.65062OpenAlexW2014450938MaRDI QIDQ1168059

Kazuo Ishihara

Publication date: 1982

Published in: Publications of the Research Institute for Mathematical Sciences, Kyoto University (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2977/prims/1195184014

zbMATH Keywords

error estimatesnumerical examplesfinite element methodsiterative methodspiecewise linear

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 (9)

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 ⋮ Successive overrelaxation method with projection for finite element solutions applied to the Dirichlet problem of the nonlinear elliptic equation \(\Delta u=bu^ 2\) ⋮ Error estimates of the lumped mass finite element method for semilinear elliptic problems ⋮ Nonlinear finite elements: sub- and supersolutions for the heterogeneous logistic equation ⋮ An \(L^{\infty}\)-error estimate for finite element solution of nonlinear elliptic problem with a source term ⋮ 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

• Uniform convergence of the upwind finite element approximation for semilinear parabolic problems
• Maximum principle and uniform convergence for the finite element method
• Iterative Solutions of the Dirichlet Problem for $\Delta u = u^2 $
• On finite element schemes of the dirichlet problem
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: Finite element approximations applied to the nonlinear boundary value problem \(\Delta(u)=b(u)^2\)