Local discontinuous Galerkin methods with implicit-explicit multistep time-marching for solving the nonlinear Cahn-Hilliard equation

DOI10.1016/j.jcp.2019.05.040zbMath1452.65249OpenAlexW2952641380WikidataQ127721768 ScholiaQ127721768MaRDI QIDQ2222320

Ying Li, Hui Shi

Publication date: 26 January 2021

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

Full work available at URL: https://doi.org/10.1016/j.jcp.2019.05.040

zbMATH Keywords

Cahn-Hilliard equationnonlinearlocal discontinuous Galerkin methodimplicit-explicit multistep scheme

Mathematics Subject Classification ID

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)

Related Items (9)

Contrast-independent partially explicit time discretizations for multiscale wave problems ⋮ Stability of high order finite difference and local discontinuous Galerkin schemes with explicit-implicit-null time-marching for high order dissipative and dispersive equations ⋮ Partially explicit time discretization for nonlinear time fractional diffusion equations ⋮ Stability of Spectral Collocation Schemes with Explicit-Implicit-Null Time-Marching for ConvectionDiffusion and Convection-Dispersion Equations ⋮ High-order semi-implicit schemes for evolutionary partial differential equations with higher order derivatives ⋮ Fully decoupled, linear and unconditional stability implicit/explicit scheme for the natural convection problem ⋮ Partially explicit splitting method for a multi-physics problem ⋮ Hybrid explicit-implicit learning for multiscale problems with time dependent source ⋮ Unconditional stability and optimal error estimates of Euler implicit/explicit-SAV scheme for the Navier-Stokes equations

Cites Work

• Implicit-explicit multistep methods for general two-dimensional nonlinear Schrödinger equations
• Energy SSP-IMEX Runge-Kutta methods for the Cahn-Hilliard equation
• On second order semi-implicit Fourier spectral methods for 2D Cahn-Hilliard equations
• Stability analysis and error estimates of local discontinuous Galerkin methods with implicit-explicit time-marching for nonlinear convection-diffusion problems
• A high-order accurate discontinuous finite element method for the numerical solution of the compressible Navier-Stokes equations
• Unconditionally stable methods for gradient flow using convex splitting Runge-Kutta scheme
• Efficient, adaptive energy stable schemes for the incompressible Cahn-Hilliard Navier-Stokes phase-field models
• Local discontinuous Galerkin methods for the generalized Zakharov system
• On large time-stepping methods for the Cahn-Hilliard equation
• TVB Runge-Kutta local projection discontinuous Galerkin finite element method for conservation laws. III: One-dimensional systems
• The Runge-Kutta discontinuous Galerkin method for conservation laws. I: Multidimensional systems
• Runge--Kutta discontinuous Galerkin methods for convection-dominated problems
• Local discontinuous Galerkin methods for partial differential equations with higher order derivatives
• Third order implicit-explicit Runge-Kutta local discontinuous Galerkin methods with suitable boundary treatment for convection-diffusion problems with Dirichlet boundary conditions
• Linear, second order and unconditionally energy stable schemes for the viscous Cahn-Hilliard equation with hyperbolic relaxation using the invariant energy quadratization method
• Stabilized linear semi-implicit schemes for the nonlocal Cahn-Hilliard equation
• Unconditional energy stability analysis of a second order implicit-explicit local discontinuous Galerkin method for the Cahn-Hilliard equation
• The scalar auxiliary variable (SAV) approach for gradient flows
• Efficient energy stable schemes for isotropic and strongly anisotropic Cahn-Hilliard systems with the Willmore regularization
• Local discontinuous Galerkin methods with explicit-implicit-null time discretizations for solving nonlinear diffusion problems
• Unconditional stability for multistep ImEx schemes: practice
• Local discontinuous Galerkin methods for the Kuramoto-Sivashinsky equations and the Ito-type coupled KdV equations
• Semi-implicit spectral deferred correction methods for highly nonlinear partial differential equations
• Local discontinuous Galerkin methods for the Cahn-Hilliard type equations
• Local discontinuous Galerkin methods with implicit-explicit time-marching for multi-dimensional convection-diffusion problems
• Stability and Error Estimates of Local Discontinuous Galerkin Methods with Implicit-Explicit Time-Marching for Advection-Diffusion Problems
• The Euler implicit/explicit scheme for the 2D time-dependent Navier-Stokes equations with smooth or non-smooth initial data
• Fully Discrete Finite Element Approximations of the Navier--Stokes--Cahn-Hilliard Diffuse Interface Model for Two-Phase Fluid Flows
• The Runge-Kutta Local Projection Discontinuous Galerkin Finite Element Method for Conservation Laws. IV: The Multidimensional Case
• TVB Runge-Kutta Local Projection Discontinuous Galerkin Finite Element Method for Conservation Laws II: General Framework
• The Local Discontinuous Galerkin Method for Time-Dependent Convection-Diffusion Systems
• Stability analysis and error estimates of local discontinuous Galerkin methods with implicit-explicit time-marching for the time-dependent fourth order PDEs
• A Local Discontinuous Galerkin Method for KdV Type Equations
• Free Energy of a Nonuniform System. I. Interfacial Free Energy
• Unconditional Stability for Multistep ImEx Schemes: Theory
• Stability and Convergence of the Crank–Nicolson/Adams–Bashforth scheme for the Time‐Dependent Navier–Stokes Equations
• Efficient linear schemes for the nonlocal Cahn-Hilliard equation of phase field models

This page was built for publication: Local discontinuous Galerkin methods with implicit-explicit multistep time-marching for solving the nonlinear Cahn-Hilliard equation