An error bound for the finite element approximation of the Cahn-Hilliard equation with logarithmic free energy

DOI10.1007/s002110050157zbMath0851.65070OpenAlexW1970410955MaRDI QIDQ1907123

James F. Blowey, John W. Barrett

Publication date: 26 November 1996

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

Full work available at URL: https://doi.org/10.1007/s002110050157

zbMATH Keywords

convergenceinitial-boundary value problemfinite elementCahn-Hilliard equationerror boundbackward Euler

Mathematics Subject Classification ID

KdV equations (Korteweg-de Vries equations) (35Q53) 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) Method of lines for initial value and initial-boundary value problems involving PDEs (65M20)

Related Items (30)

Existence and Uniqueness for a Model Describing Chalcopyrite Disease within Sphalerite ⋮ A practical numerical scheme for the ternary Cahn-Hilliard system with a logarithmic free energy ⋮ An improved error bound for a finite element approximation of a reaction-diffusion system of \(\lambda\)-\(\omega\) type ⋮ Unnamed Item ⋮ New models of Cahn-Hilliard-Gurtin equations ⋮ On a system of nonlinear partial differential equations ⋮ Second order convex splitting schemes for periodic nonlocal Cahn-Hilliard and Allen-Cahn equations ⋮ Conservative nonlinear difference scheme for the Cahn-Hilliard equation ⋮ Numerical investigation into the dependence of the Allen-Cahn equation on the free energy ⋮ An optimal error bound for a finite element approximation of spatially extended predator-prey interaction model ⋮ Positivity-preserving, energy stable numerical schemes for the Cahn-Hilliard equation with logarithmic potential ⋮ A three level linearized compact difference scheme for the Cahn-Hilliard equation ⋮ A numerical method based on the boundary integral equation and dual reciprocity methods for one-dimensional Cahn-Hilliard equation ⋮ Error control for the approximation of Allen-Cahn and Cahn-Hilliard equations with a logarithmic potential ⋮ The Cahn-Hilliard equation with logarithmic potentials ⋮ Finite element approximation of the Cahn-Hilliard equation on surfaces ⋮ Unconditionally energy stable discontinuous Galerkin schemes for the Cahn-Hilliard equation ⋮ A discontinuous Galerkin method for the Cahn-Hilliard equation ⋮ Optimal distributed control of nonlinear Cahn-Hilliard systems with computational realization ⋮ Decoupled, EnergyStableNumericalSchemeforthe Cahn-Hilliard-Hele-Shaw System with Logarithmic Flory-Huggins Potential ⋮ Error estimates and adaptive finite element methods ⋮ A three level finite element approximation of a pattern formation model in developmental biology ⋮ Goal-oriented error estimation for Cahn-Hilliard models of binary phase transition ⋮ Numerical analysis for the Cahn-Hilliard-Hele-Shaw system with variable mobility and logarithmic Flory-Huggins potential ⋮ An adaptive finite-element Moreau–Yosida-based solver for a non-smooth Cahn–Hilliard problem ⋮ Stability analysis and best approximation error estimates of discontinuous time-stepping schemes for the Allen–Cahn equation ⋮ Finite element analysis of nonlinear reaction-diffusion system of Fitzhugh-Nagumo type with Robin boundary conditions ⋮ Convergence to equilibrium for time and space discretizations of the Cahn-Hilliard equation ⋮ A second-order Strang splitting scheme with exponential integrating factor for the Allen-Cahn equation with logarithmic Flory-Huggins potential ⋮ A Second Order Accurate in Time, Energy Stable Finite Element Scheme for the Flory-Huggins-Cahn-Hilliard Equation

This page was built for publication: An error bound for the finite element approximation of the Cahn-Hilliard equation with logarithmic free energy