Finite element approximation of a model reaction-diffusion problem with a non-Lipschitz nonlinearity

DOI10.1007/BF01385777zbMath0735.65078MaRDI QIDQ1174960

Robert M. Shanahan, John W. Barrett

Publication date: 25 June 1992

Published in: Numerische Mathematik (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/133546

zbMATH Keywords

global convergenceGalerkin methodfinite element approximationsuccessive overrelaxationreaction-diffusion equationoptimal error boundsnonlinear SOR algorithm

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 (10)

Bounding the error for approximate solutions of almost linear complementarity problems using feasible vectors ⋮ A fixed-point method for a class of super-large scale nonlinear complementarity problems ⋮ Finite element approximation of a non-Lipschitz nonlinear eigenvalue problem ⋮ A full-Newton step non-interior continuation algorithm for a class of complementarity problems ⋮ An algorithm for a class of nonlinear complementarity problems with non-Lipschitzian functions ⋮ A regularized projection method for complementarity problems with non-Lipschitzian functions ⋮ A Finite Algorithm for Almost Linear Complementarity Problems ⋮ An accelerated monotonic convergent algorithm for a class of non-Lipschitzian NCP\((F)\) involving an \(M\)-matrix ⋮ Components identification based method for box constrained variational inequality problems with almost linear functions ⋮ Numerical methods for nonlinear equations

Cites Work

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• Numerical methods for reaction-diffusion problems with non-differentiable kinetics
• Sharp \(L^{\infty}\)-error estimates for semilinear elliptic problems with free boundaries
• Maximum principle and uniform convergence for the finite element method
• Hausdoff measure estimates of a free boundary for a minimum problem
• Diffusion and reaction with monotone kinetics
• The Free Boundary of a Semilinear Elliptic Equation
• Superconvergent Recovery of the Gradient from Piecewise Linear Finite-element Approximations
• A note on the approximation of free boundaries by finite element methods
• Polynomial Approximation of Functions in Sobolev Spaces
• On the Finite Element Approximation of an Elliptic Variational Inequality Arising from an Implicit Time Discretization of the Stefan Problem

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