Unconditionally energy stable invariant energy quadratization finite element methods for phase-field crystal equation and Swift-Hohenberg equation

Initial-boundary value problems for higher-order parabolic equations (35K35) Stability and convergence of numerical methods for boundary value problems involving PDEs (65N12) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30)

Cites Work

Linearly first- and second-order, unconditionally energy stable schemes for the phase field crystal model
Convergence analysis and numerical implementation of a second order numerical scheme for the three-dimensional phase field crystal equation
A new space-time discretization for the Swift-Hohenberg equation that strictly respects the Lyapunov functional
Efficient numerical schemes with unconditional energy stabilities for the modified phase field crystal equation
Linear second order energy stable schemes for phase field crystal growth models with nonlocal constraints
A second order energy stable BDF numerical scheme for the Swift-Hohenberg equation
High order unconditionally energy stable RKDG schemes for the Swift-Hohenberg equation
Optimal error estimates of the local discontinuous Galerkin method and high-order time discretization scheme for the Swift-Hohenberg equation
Energy dissipation-preserving time-dependent auxiliary variable method for the phase-field crystal and the Swift-Hohenberg models
A novel second-order time accurate fully discrete finite element scheme with decoupling structure for the hydrodynamically-coupled phase field crystal model
Stability and convergence analysis of adaptive BDF2 scheme for the Swift-Hohenberg equation
Stability and error estimates of the SAV Fourier-spectral method for the phase field crystal equation
Efficient modified stabilized invariant energy quadratization approaches for phase-field crystal equation
Two fast and efficient linear semi-implicit approaches with unconditional energy stability for nonlocal phase field crystal equation
An efficient and stable compact fourth-order finite difference scheme for the phase field crystal equation
Unconditionally energy stable DG schemes for the Swift-Hohenberg equation
An energy-stable second-order finite element method for the Swift-Hohenberg equation
Numerical approximations for a new \(L^2\)-gradient flow based phase field crystal model with precise nonlocal mass conservation
Convergence Analysis of a Second Order Convex Splitting Scheme for the Modified Phase Field Crystal Equation
An Energy-Stable and Convergent Finite-Difference Scheme for the Phase Field Crystal Equation
An Energy Stable BDF2 Fourier Pseudo-Spectral Numerical Scheme for the Square Phase Field Crystal Equation

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