Numerical solutions of singularly perturbed reaction diffusion equation with Sobolev gradients

DOI10.1155/2013/542897zbMath1287.65082OpenAlexW2100913482WikidataQ59014372 ScholiaQ59014372MaRDI QIDQ2443727

Nauman Raza, Asma Rashid Butt

Publication date: 8 April 2014

Published in: Journal of Function Spaces and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1155/2013/542897

zbMATH Keywords

singular perturbationfinite element methodreaction diffusion modelSobolev gradient method

Mathematics Subject Classification ID

Singular perturbations in context of PDEs (35B25) Reaction-diffusion equations (35K57) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60)

Uses Software

• FreeFem++

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Numerical solution of Burgers equation by the Sobolev gradient method
• Approximate solutions to Poisson-Boltzmann systems with Sobolev gradients
• Preconditioning operators and Sobolev gradients for nonlinear elliptic problems
• Sobolev gradient preconditioning for the electrostatic potential equation
• Approximating time evolution related to Ginzburg-Landau functionals via Sobolev gradient methods in a finite-element setting
• Application of Sobolev gradient method to Poisson-Boltzmann system
• Sobolev gradient approach for the time evolution related to energy minimization of Ginzburg-Landau functionals
• Energy minimization related to the nonlinear Schrödinger equation
• Energy minimization using Sobolev gradients: application to phase separation and ordering.
• A quasi-local Gross-Pitaevskii equation for attractive Bose-Einstein condensates
• Sobolev preconditioning for the Poisson-Boltzmann equation
• Constructing fair curves and surfaces with a Sobolev gradient method
• A variational approach to an elastic inverse problem
• Steady-state convection-diffusion problems
• Sobolev gradient preconditioning for image‐processing PDEs
• Uniform approximation of singularly perturbed reaction-diffusion problems by the finite element method on a Shishkin mesh
• Sobolev gradients and differential equations

This page was built for publication: Numerical solutions of singularly perturbed reaction diffusion equation with Sobolev gradients