A multigrid method for the Cahn-Hilliard equation with obstacle potential

DOI10.1016/j.amc.2009.03.036zbMath1168.65386OpenAlexW1968029546MaRDI QIDQ1029362

Ľubomír Baňas, Robert Nürnberg

Publication date: 10 July 2009

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

Full work available at URL: https://doi.org/10.1016/j.amc.2009.03.036

zbMATH Keywords

convergencefinite elementsnumerical examplesCahn-Hilliard equationmultigrid methodobstacle free energy

Mathematics Subject Classification ID

KdV equations (Korteweg-de Vries equations) (35Q53) 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) Multigrid methods; domain decomposition for initial value and initial-boundary value problems involving PDEs (65M55)

Related Items

Fast multilevel solvers for a class of discrete fourth order parabolic problems, Fast solution of Cahn-Hilliard variational inequalities using implicit time discretization and finite elements, Upper bounds for coarsening for the deep quench obstacle problem, A novel method to impose boundary conditions for higher-order partial differential equations, The Cahn-Hilliard equation with logarithmic potentials, On the stable discretization of strongly anisotropic phase field models with applications to crystal growth, Primal‐dual active set methods for Allen–Cahn variational inequalities with nonlocal constraints, An adaptive finite-element Moreau–Yosida-based solver for a non-smooth Cahn–Hilliard problem, Solving the Cahn-Hilliard variational inequality with a semi-smooth Newton method, Allen-Cahn and Cahn-Hilliard Variational Inequalities Solved with Optimization Techniques, The Cahn-Hilliard equation and some of its variants

Uses Software

• ALBERTA

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Phase field computations for surface diffusion and void electromigration in \({\mathbb{R}^3}\)
• Finite element approximation of a three dimensional phase field model for void electromigration
• A multilevel iterative method for symmetric, positive definite linear complementarity problems
• An octree multigrid method for quasi-static Maxwell's equations with highly discontinuous coefficients
• Gradient theory of phase transitions with boundary contact energy
• On multi-grid methods for variational inequalities
• Monotone multigrid methods for elliptic variational inequalities. I
• On Schwarz-type smoothers for saddle point problems
• Conservative multigrid methods for Cahn--Hilliard fluids.
• Design of adaptive finite element software. The finite element toolbox ALBERTA. With CD-ROM
• Numerical analysis of the Cahn-Hilliard equation and approximation for the Hele-Shaw problem
• Convergence of the Cahn-Hilliard equation to the Hele-Shaw model
• Discretized obstacle problems with penalties on nested grids
• A multigrid finite element solver for the Cahn-Hilliard equation
• Multigrid Algorithms for Variational Inequalities
• The Cahn–Hilliard gradient theory for phase separation with non-smooth free energy Part II: Numerical analysis
• Finite Element Approximation of a Phase Field Model for Void Electromigration
• The Cahn–Hilliard equation with a concentration dependent mobility: motion by minus the Laplacian of the mean curvature
• Finite Element Approximation of the Cahn--Hilliard Equation with Degenerate Mobility
• Free Energy of a Nonuniform System. I. Interfacial Free Energy
• Numerical Analysis of Vanka‐Type Solvers for Steady Stokes and Navier–Stokes Flows
• Multilevel projection algorithm for solving obstacle problems