A multi-physical structure-preserving method and its analysis for the conservative Allen-Cahn equation with nonlocal constraint
DOI10.1007/s11075-024-01757-4MaRDI QIDQ6624873
Xu Liu, Yuezheng Gong, Qi Hong, Hong-lin Liao
Publication date: 28 October 2024
Published in: Numerical Algorithms (Search for Journal in Brave)
error estimateconservative Allen-Cahn equationmaximum bound principleenergy dissipation lawmulti-physical structure-preserving method
Integro-partial differential equations (45K05) Maximum principles in context of PDEs (35B50) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs (65M70) Error bounds for initial value and initial-boundary value problems involving PDEs (65M15) Finite difference methods for boundary value problems involving PDEs (65N06) Mesh generation, refinement, and adaptive methods for the numerical solution of initial value and initial-boundary value problems involving PDEs (65M50) Integro-partial differential equations (35R09)
Cites Work
- Unnamed Item
- Unnamed Item
- An adaptive time-stepping strategy for solving the phase field crystal model
- Numerical study of heat transfer characteristics of the micropolar boundary layer near a stagnation point on a moving wall
- Mass conserving Allen-Cahn equation and volume preserving mean curvature flow
- Arbitrarily high order structure-preserving algorithms for the Allen-Cahn model with a nonlocal constraint
- Computation of multiphase systems with phase field models.
- A conservative Allen-Cahn equation with a space-time dependent Lagrange multiplier
- A stable and structure-preserving scheme for a non-local Allen-Cahn equation
- Numerical approximations for the molecular beam epitaxial growth model based on the invariant energy quadratization method
- The scalar auxiliary variable (SAV) approach for gradient flows
- Supplementary variable method for structure-preserving approximations to partial differential equations with deduced equations
- Linear energy stable and maximum principle preserving semi-implicit scheme for Allen-Cahn equation with double well potential
- Unconditionally maximum bound principle preserving linear schemes for the conservative Allen-Cahn equation with nonlocal constraint
- A high-order and unconditionally energy stable scheme for the conservative Allen-Cahn equation with a nonlocal Lagrange multiplier
- A maximum bound principle preserving iteration technique for a class of semilinear parabolic equations
- Stability and convergence of Strang splitting. I: Scalar Allen-Cahn equation
- A gPAV-based unconditionally energy-stable scheme for incompressible flows with outflow/open boundaries
- A new Lagrange multiplier approach for gradient flows
- Supplementary variable method for thermodynamically consistent partial differential equations
- Second order linear energy stable schemes for Allen-Cahn equations with nonlocal constraints
- Numerical analysis of fully discretized Crank-Nicolson scheme for fractional-in-space Allen-Cahn equations
- A new Lagrange multiplier approach for constructing structure preserving schemes. I: Positivity preserving
- Second-order Convex Splitting Schemes for Gradient Flows with Ehrlich–Schwoebel Type Energy: Application to Thin Film Epitaxy
- A modified phase field approximation for mean curvature flow with conservation of the volume
- An Energy Stable and Convergent Finite-Difference Scheme for the Modified Phase Field Crystal Equation
- An Adaptive Time-Stepping Strategy for the Molecular Beam Epitaxy Models
- Numerical Analysis of a Continuum Model of Phase Transition
- Nonlocal reaction—diffusion equations and nucleation
- Volume-Preserving Mean Curvature Flow as a Limit of a Nonlocal Ginzburg-Landau Equation
- Maximum Principle Preserving Exponential Time Differencing Schemes for the Nonlocal Allen--Cahn Equation
- Maximum Bound Principles for a Class of Semilinear Parabolic Equations and Exponential Time-Differencing Schemes
- A New Lagrange Multiplier Approach for Constructing Structure Preserving Schemes, II. Bound Preserving
- On Energy Stable, Maximum-Principle Preserving, Second-Order BDF Scheme with Variable Steps for the Allen--Cahn Equation
- A diffuse domain method for two-phase flows with large density ratio in complex geometries
- Free Energy of a Nonuniform System. I. Interfacial Free Energy
- A New Class of Efficient and Robust Energy Stable Schemes for Gradient Flows
- Implicit-Explicit Scheme for the Allen-Cahn Equation Preserves the Maximum Principle
- A unified discontinuous Galerkin framework for time integration
- A new class of energy-preserving numerical integration methods
- Geometric Numerical Integration
- Stability Analysis of Large Time‐Stepping Methods for Epitaxial Growth Models
- A stable and conservative finite difference scheme for the Cahn-Hilliard equation
This page was built for publication: A multi-physical structure-preserving method and its analysis for the conservative Allen-Cahn equation with nonlocal constraint
