Optimal \(L^{\infty}\) error estimates for finite element Galerkin methods for nonlinear evolution equations

DOI10.1007/s12190-007-0018-zzbMath1156.65081OpenAlexW2023367387MaRDI QIDQ949256

Khaled Omrani

Publication date: 21 October 2008

Published in: Journal of Applied Mathematics and Computing (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s12190-007-0018-z

zbMATH Keywords

stabilityconvergenceGalerkin methodheat equationlinearizationreaction-diffusion equationCrank-Nicolson methodKuramoto-Tsuzuki equationnonlinear nonstationary initial-boundary problems

Mathematics Subject Classification ID

Nonlinear parabolic equations (35K55) Reaction-diffusion equations (35K57) Heat equation (35K05) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Error bounds for initial value and initial-boundary value problems involving PDEs (65M15)

Related Items (8)

Numerical methods and error analysis for the nonlinear Sivashinsky equation ⋮ Multilevel augmentation methods for solving the Burgers' equation ⋮ More accurate results for nonlinear generalized Benjamin-Bona-Mahony-Burgers (GBBMB) problem through spectral meshless radial point interpolation (SMRPI) ⋮ The numerical solution of nonlinear high dimensional generalized Benjamin-Bona-Mahony-Burgers equation via the meshless method of radial basis functions ⋮ Stability and convergence of difference scheme for nonlinear evolutionary type equations ⋮ A robust semi-explicit difference scheme for the Kuramoto-Tsuzuki equation ⋮ The use of interpolating element-free Galerkin technique for solving 2D generalized Benjamin-Bona-Mahony-Burgers and regularized long-wave equations on non-rectangular domains with error estimate ⋮ A new approach for numerical solution of Kuramoto-Tsuzuki equation

Cites Work

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• Galerkin Methods for Singular Boundary Value Problems in One Space Dimension
• On the Quasi-Optimality in $L_\infty$ of the $\overset{\circ}{H}^1$-Projection into Finite Element Spaces*
• Finite difference discretization of the cubic Schrödinger equation
• Three-Level Galerkin Methods for Parabolic Equations
• On the numerical approach of the enthalpy method for the Stefan problem
• A finite element method for the Sivashinsky equation

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