Energy stable and convergent finite element schemes for the modified phase field crystal equation
From MaRDI portal
Publication:2830707
DOI10.1051/m2an/2015092zbMath1358.82025OpenAlexW2522634436MaRDI QIDQ2830707
Morgan Pierre, Maurizio Grasselli
Publication date: 28 October 2016
Published in: ESAIM: Mathematical Modelling and Numerical Analysis (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1051/m2an/2015092
finite elementsŁojasiewicz inequalitysecond-order schemesgradient-like systemsmodified phase field crystal equation
Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Numerical nonlinear stabilities in dynamical systems (65P40) Crystals in solids (74N05) Dynamic and nonequilibrium phase transitions (general) in statistical mechanics (82C26) PDEs in connection with statistical mechanics (35Q82)
Related Items
A linearly second-order, unconditionally energy stable scheme and its error estimates for the modified phase field crystal equation, Efficient unconditionally stable numerical schemes for a modified phase field crystal model with a strong nonlinear vacancy potential, Efficient modified stabilized invariant energy quadratization approaches for phase-field crystal equation, Linear and unconditionally energy stable schemes for the modified phase field crystal equation, Error estimates for second-order SAV finite element method to phase field crystal model, Efficient second-order unconditionally stable numerical schemes for the modified phase field crystal model with long-range interaction, Convergence analysis and numerical implementation of a second order numerical scheme for the three-dimensional phase field crystal equation, Novel linear decoupled and unconditionally energy stable numerical methods for the modified phase field crystal model, Efficient numerical schemes with unconditional energy stabilities for the modified phase field crystal equation, Two fast and efficient linear semi-implicit approaches with unconditional energy stability for nonlocal phase field crystal equation, Error estimates for the scalar auxiliary variable (SAV) schemes to the modified phase field crystal equation, \(C^1 \)-VEM for some variants of the Cahn-Hilliard equation: a numerical exploration, Convergence to equilibrium for time and space discretizations of the Cahn-Hilliard equation, Convergence to equilibrium for a second-order time semi-discretization of the Cahn-Hilliard equation, The Cahn-Hilliard equation and some of its variants, REMARKS ON THE ASYMPTOTIC BEHAVIOR OF SCALAR AUXILIARY VARIABLE (SAV) SCHEMES FOR GRADIENT-LIKE FLOWS
Uses Software
Cites Work
- Robust exponential attractors for the modified phase-field crystal equation
- An unconditionally energy-stable method for the phase field crystal equation
- Energy stable and efficient finite-difference nonlinear multigrid schemes for the modified phase field crystal equation
- On the 3D Cahn-Hilliard equation with inertial term
- Provably unconditionally stable, second-order time-accurate, mixed variational methods for phase-field models
- Global smooth solutions of the three-dimensional modified phase field crystal equation
- Stable and efficient finite-difference nonlinear-multigrid schemes for the phase field crystal equation
- Convergence to equilibrium for the backward Euler scheme and applications
- Instability of spatially periodic patterns due to a zero mode in the phase-field crystal equation
- Compact sets in the space \(L^ p(0,T;B)\)
- Convergence for semilinear degenerate parabolic equations in several space dimensions
- Convergence to equilibrium of solutions of the backward Euler scheme for asymptotically autonomous second-order gradient-like systems
- Steady state bifurcations for phase field crystal equations with underlying two dimensional kernel
- Convergence to equilibrium for discretized gradient-like systems with analytic features
- Convergence Analysis of a Second Order Convex Splitting Scheme for the Modified Phase Field Crystal Equation
- Well-posedness and long-time behavior for the modified phase-field crystal equation
- Stationary solutions to phase field crystal equations
- An Energy Stable and Convergent Finite-Difference Scheme for the Modified Phase Field Crystal Equation
- A SPLITTING METHOD FOR THE CAHN–HILLIARD EQUATION WITH INERTIAL TERM
- Trajectory and smooth attractors for Cahn–Hilliard equations with inertial term
- Characterizations of Łojasiewicz inequalities: Subgradient flows, talweg, convexity
- An Energy-Stable and Convergent Finite-Difference Scheme for the Phase Field Crystal Equation
- On the 2D Cahn–Hilliard Equation with Inertial Term
- New development in freefem++
- A simple and efficient scheme for phase field crystal simulation
- Convergence in gradient-like systems which are asymptotically autonomous and analytic
