Approximating time evolution related to Ginzburg-Landau functionals via Sobolev gradient methods in a finite-element setting

DOI10.1016/j.jcp.2009.10.048zbMath1181.65124OpenAlexW1978403133MaRDI QIDQ846587

Sultan Sial, Nauman Raza, Shahid S. Siddiqi

Publication date: 9 February 2010

Published in: Journal of Computational Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jcp.2009.10.048

zbMATH Keywords

Sobolev gradientmodel A

Mathematics Subject Classification ID

Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60)

Related Items (14)

Unconditionally energy stable time stepping scheme for Cahn-Morral equation: application to multi-component spinodal decomposition and optimal space tiling ⋮ Numerical approximation of time evolution related to Ginzburg-Landau functionals using weighted Sobolev gradients ⋮ A finite element method with mesh adaptivity for computing vortex states in fast-rotating Bose-Einstein condensates ⋮ Optical tomography reconstruction algorithm with the finite element method: an optimal approach with regularization tools ⋮ An efficient fully linearized semi-implicit Galerkin-mixed FEM for the dynamical Ginzburg-Landau equations of superconductivity ⋮ Computationally efficient approach for the minimization of volume constrained vector-valued Ginzburg-Landau energy functional ⋮ Single-iteration Sobolev descent for linear initial value problems ⋮ A link between the steepest descent method and fixed-point iterations ⋮ Numerical solution of Burgers equation by the Sobolev gradient method ⋮ Numerical solutions of singularly perturbed reaction diffusion equation with Sobolev gradients ⋮ Efficient Numerical Solution of Dynamical Ginzburg-Landau Equations under the Lorentz Gauge ⋮ A New Mixed Formulation and Efficient Numerical Solution of Ginzburg--Landau Equations Under the Temporal Gauge ⋮ A stabilized semi-implicit Euler gauge-invariant method for the time-dependent Ginzburg-Landau equations ⋮ Polynomial solution of singular differential equations using Weighted Sobolev gradients

Uses Software

• FreeFem++

Cites Work

• On the recovery of transport parameters in groundwater modelling
• Preconditioning operators and Sobolev gradients for nonlinear elliptic problems
• Sobolev gradient preconditioning for the electrostatic potential equation
• Sobolev gradient approach for the time evolution related to energy minimization of Ginzburg-Landau functionals
• 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
• A variational approach to an elastic inverse problem
• Recursive form of Sobolev gradient method for ODEs on long intervals
• Free Energy of a Nonuniform System. I. Interfacial Free Energy
• Sobolev gradients and differential equations
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