Arbitrarily high order and fully discrete extrapolated RK-SAV/DG schemes for phase-field gradient flows
DOI10.1007/s10915-022-01995-5zbMath1497.65182OpenAlexW4295996003MaRDI QIDQ2676804
Publication date: 28 September 2022
Published in: Journal of Scientific Computing (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/s10915-022-01995-5
Cahn-Hilliard equationphase-field modelsAllen-Cahn equationenergy stabilitygradient flowsconvergence and error analysis
PDEs in connection with fluid mechanics (35Q35) Error bounds for boundary value problems involving PDEs (65N15) 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) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06)
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Cites Work
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- Numerical approximations of Allen-Cahn and Cahn-Hilliard equations
- Galerkin finite element methods for parabolic problems
- Linear, first and second-order, unconditionally energy stable numerical schemes for the phase field model of homopolymer blends
- 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
- Three-dimensional multispecies nonlinear tumor growth. II: Tumor invasion and angiogenesis
- Arbitrarily high-order maximum bound preserving schemes with cut-off postprocessing for Allen-Cahn equations
- Energy-decreasing exponential time differencing Runge-Kutta methods for phase-field models
- Stability and convergence of Strang splitting. I: Scalar Allen-Cahn equation
- A new Lagrange multiplier approach for gradient flows
- A local discontinuous Galerkin method for the Korteweg-de Vries equation with boundary effect
- An A Priori Error Analysis of the Local Discontinuous Galerkin Method for Elliptic Problems
- Superconvergence of the Local Discontinuous Galerkin Method for Elliptic Problems on Cartesian Grids
- High Order Local Discontinuous Galerkin Methods for the Allen-Cahn Equation: Analysis and Simulation
- Second-order Convex Splitting Schemes for Gradient Flows with Ehrlich–Schwoebel Type Energy: Application to Thin Film Epitaxy
- The phase field method for geometric moving interfaces and their numerical approximations
- Long Time Numerical Simulations for Phase-Field Problems Using $p$-Adaptive Spectral Deferred Correction Methods
- Discontinuous Galerkin Methods for Solving Elliptic and Parabolic Equations
- The Local Discontinuous Galerkin Method for Time-Dependent Convection-Diffusion Systems
- Unified Analysis of Discontinuous Galerkin Methods for Elliptic Problems
- Multiple Scalar Auxiliary Variable (MSAV) Approach and its Application to the Phase-Field Vesicle Membrane Model
- A diffuse-interface method for simulating two-phase flows of complex fluids
- DIFFUSE-INTERFACE METHODS IN FLUID MECHANICS
- Maximum Bound Principles for a Class of Semilinear Parabolic Equations and Exponential Time-Differencing Schemes
- A Highly Efficient and Accurate New Scalar Auxiliary Variable Approach for Gradient Flows
- Energy-Decaying Extrapolated RK--SAV Methods for the Allen--Cahn and Cahn--Hilliard Equations
- Free Energy of a Nonuniform System. I. Interfacial Free Energy
- Numerical error analysis for nonsymmetric interior penalty discontinuous Galerkin method of Cahn–Hilliard equation
- A New Class of Efficient and Robust Energy Stable Schemes for Gradient Flows
- Fourth-Order Time-Stepping for Stiff PDEs
- Numerical approximations for a three-component Cahn–Hilliard phase-field model based on the invariant energy quadratization method
- Stability Analysis of Large Time‐Stepping Methods for Epitaxial Growth Models
