DOI10.1137/110822839zbMath1247.65088OpenAlexW2030350543MaRDI QIDQ2882335
Jie Shen, Cheng Wang, Xiaoming Wang, Steven M. Wise
Publication date: 4 May 2012
Published in: SIAM Journal on Numerical Analysis (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1137/110822839
New epitaxial thin‐film models and numerical approximation ⋮
An Energy Stable Filtered Backward Euler Scheme for the MBE Equation with Slope Selection ⋮
A Stable Arbitrarily High Order Time-Stepping Method for Thermal Phase Change Problems ⋮
Optimal Error Estimates of the Semi-Discrete Local Discontinuous Galerkin Method and Exponential Time Differencing Schemes for the Thin Film Epitaxy Problem Without Slope Selection ⋮
Optimized Schwarz Methods for the Cahn–Hilliard Equation ⋮
An adaptive time-stepping method for the phase-field molecular beam epitaxial growth model on evolving surfaces ⋮
Efficient and linear schemes for anisotropic Cahn-Hilliard model using the stabilized-invariant energy quadratization (S-IEQ) approach ⋮
Gauge-Uzawa-based, highly efficient decoupled schemes for the diffuse interface model of two-phase magnetohydrodynamic ⋮
An efficient energy-stable pseudospectral method for simulating vortex dynamics of the Ginzburg-Landau-Schrödinger equation ⋮
Efficient and accurate exponential SAV algorithms with relaxation for dissipative system ⋮
Accurate and efficient algorithms with unconditional energy stability for the time fractional Cahn–Hilliard and Allen–Cahn equations ⋮
A general class of linear unconditionally energy stable schemes for the gradient flows. II. ⋮
Conservative unconditionally stable decoupled numerical schemes for the <scp>Cahn–Hilliard–Navier–Stokes–Darcy–Boussinesq</scp> system ⋮
An efficient and physically consistent numerical method for the Maxwell–Stefan–Darcy model of two‐phase flow in porous media ⋮
A fully decoupled numerical method for Cahn-Hilliard-Navier-Stokes-Darcy equations based on auxiliary variable approaches ⋮
A new high-order maximum-principle-preserving explicit Runge-Kutta method for the nonlocal Allen-Cahn equation ⋮
A second order accurate, positivity preserving numerical method for the Poisson-Nernst-Planck system and its convergence analysis ⋮
A SAV finite element method for the Cahn-Hilliard equation with dynamic boundary conditions ⋮
High-order supplementary variable methods for thermodynamically consistent partial differential equations ⋮
Numerical algorithms of subdivision-based IGA-EIEQ method for the molecular beam epitaxial growth models on complex surfaces ⋮
High order accurate and convergent numerical scheme for the strongly anisotropic Cahn–Hilliard model ⋮
The fast scalar auxiliary variable approach with unconditional energy stability for nonlocal Cahn–Hilliard equation ⋮
A New Class of Efficient SAV Schemes with Lagrange Multipliers for Dissipative Systems with Global Constraints ⋮
Reformulated Weak Formulation and Efficient Fully Discrete Finite Element Method for a Two-Phase Ferrohydrodynamics Shliomis Model ⋮
Efficient and energy stable numerical schemes for the two-mode phase field crystal equation ⋮
A fully-decoupled artificial compressible Crank-Nicolson-leapfrog time stepping scheme for the phase field model of two-phase incompressible flows ⋮
The robust physics-informed neural networks for a typical fourth-order phase field model ⋮
On a novel fully-decoupled, linear and second-order accurate numerical scheme for the Cahn-Hilliard-Darcy system of two-phase Hele-Shaw flow ⋮
A Ginzburg-Landau-\({H}^{-1}\) model and its SAV algorithm for image inpainting ⋮
A deep learning method for the dynamics of classic and conservative Allen-Cahn equations based on fully-discrete operators ⋮
Numerical analysis of a second-order energy-stable finite element method for the Swift-Hohenberg equation ⋮
A second-order exponential time differencing multi-step energy stable scheme for Swift-Hohenberg equation with quadratic-cubic nonlinear term ⋮
A linear second-order maximum bound principle-preserving BDF scheme for the Allen-Cahn equation with a general mobility ⋮
Errors of an Implicit Variable-Step BDF2 Method for a Molecular Beam Epitaxial Model with Slope Selection ⋮
Double stabilizations and convergence analysis of a second-order linear numerical scheme for the nonlocal Cahn-Hilliard equation ⋮
Approximation of multiphase mean curvature flows with arbitrary nonnegative mobilities ⋮
Positivity-preserving, energy stable numerical schemes for the Cahn-Hilliard equation with logarithmic potential ⋮
Stability analysis of several time discrete schemes for Allen-Cahn and Cahn-Hilliard equations ⋮
A Physics-Informed Structure-Preserving Numerical Scheme for the Phase-Field Hydrodynamic Model of Ternary Fluid Flows ⋮
A positivity-preserving, energy stable BDF2 scheme with variable steps for the Cahn-Hilliard equation with logarithmic potential ⋮
Fully discrete discontinuous Galerkin numerical scheme with second-order temporal accuracy for the hydrodynamically coupled lipid vesicle model ⋮
Second order stabilized semi-implicit scheme for the Cahn-Hilliard model with dynamic boundary conditions ⋮
Energy stable and convergent BDF3-5 schemes for the molecular beam epitaxial model with slope selection ⋮
Discontinuous Galerkin methods for network patterning phase-field models ⋮
A BDF2 energy‐stable scheme for the binary fluid‐surfactant hydrodynamic model ⋮
A Hessian Recovery Based Linear Finite Element Method for Molecular Beam Epitaxy Growth Model with Slope Selection ⋮
Error analysis of second-order IEQ numerical schemes for the viscous Cahn-Hilliard equation with hyperbolic relaxation ⋮
Fast High Order and Energy Dissipative Schemes with Variable Time Steps for Time-Fractional Molecular Beam Epitaxial Growth Model ⋮
The subdivision-based IGA-EIEQ numerical scheme for the Cahn-Hilliard-Darcy system of two-phase Hele-Shaw flow on complex curved surfaces ⋮
A Scalar Auxiliary Variable (SAV) Finite Element Numerical Scheme for the Cahn-Hilliard-Hele-Shaw System with Dynamic Boundary Conditions ⋮
Numerical approximations for a three-component Cahn–Hilliard phase-field model based on the invariant energy quadratization method ⋮
Unnamed Item ⋮
Energy stability and convergence of SAV block-centered finite difference method for gradient flows ⋮
Stability and convergence of second-order schemes for the nonlinear epitaxial growth model without slope selection ⋮
Decoupled, Linear, and Unconditionally Energy Stable Fully Discrete Finite Element Numerical Scheme for a Two-Phase Ferrohydrodynamics Model ⋮
Adaptive Second-Order Crank--Nicolson Time-Stepping Schemes for Time-Fractional Molecular Beam Epitaxial Growth Models ⋮
Convex Splitting Method for Strongly Anisotropic Solid-State Dewetting Problems in Two Dimensions ⋮
A novel second-order time accurate fully discrete finite element scheme with decoupling structure for the hydrodynamically-coupled phase field crystal model ⋮
Arbitrarily high order structure-preserving algorithms for the Allen-Cahn model with a nonlocal constraint ⋮
A computational model of protein induced membrane morphology with geodesic curvature driven protein-membrane interface ⋮
An integral equation method for the Cahn-Hilliard equation in the wetting problem ⋮
Arbitrarily high-order linear energy stable schemes for gradient flow models ⋮
A linearly second-order, unconditionally energy stable scheme and its error estimates for the modified phase field crystal equation ⋮
A positive and energy stable numerical scheme for the Poisson-Nernst-Planck-Cahn-Hilliard equations with steric interactions ⋮
Analysis of the second-order BDF scheme with variable steps for the molecular beam epitaxial model without slope selection ⋮
Maximum bound principle preserving integrating factor Runge-Kutta methods for semilinear parabolic equations ⋮
Stabilized semi-implicit numerical schemes for the Cahn-Hilliard-like equation with variable interfacial parameter ⋮
A structure-preserving, operator splitting scheme for reaction-diffusion equations with detailed balance ⋮
Global well-posedness for the 4D epitaxial growth models ⋮
Second-order decoupled energy-stable schemes for Cahn-Hilliard-Navier-Stokes equations ⋮
Second order linear decoupled energy dissipation rate preserving schemes for the Cahn-Hilliard-extended-Darcy model ⋮
Robust and stable schemes for time fractional molecular beam epitaxial growth model using SAV approach ⋮
High order, semi-implicit, energy stable schemes for gradient flows ⋮
A highly efficient and accurate exponential semi-implicit scalar auxiliary variable (ESI-SAV) approach for dissipative system ⋮
Unconditionally stable numerical methods for Cahn-Hilliard-Navier-Stokes-Darcy system with different densities and viscosities ⋮
Improving the accuracy and consistency of the scalar auxiliary variable (SAV) method with relaxation ⋮
A second-order time accurate and fully-decoupled numerical scheme of the Darcy-Newtonian-nematic model for two-phase complex fluids confined in the Hele-Shaw cell ⋮
An energy stable linear numerical method for thermodynamically consistent modeling of two-phase incompressible flow in porous media ⋮
A second order in time, decoupled, unconditionally stable numerical scheme for the Cahn-Hilliard-Darcy system ⋮
Linear second order in time energy stable schemes for hydrodynamic models of binary mixtures based on a spatially pseudospectral approximation ⋮
Energy stability of BDF methods up to fifth-order for the molecular beam epitaxial model without slope selection ⋮
Global-in-time Gevrey regularity solution for a class of bistable gradient flows ⋮
On novel linear schemes for the Cahn-Hilliard equation based on an improved invariant energy quadratization approach ⋮
A metric-based approach to multiphase mean curvature flows with mobilities ⋮
Semi-discrete energy-stable schemes for a tensor-based hydrodynamic model of nematic liquid crystal flows ⋮
Numerical methods for solving the Cahn-Hilliard equation and its applicability to related energy-based models ⋮
Energy stable and efficient finite-difference nonlinear multigrid schemes for the modified phase field crystal equation ⋮
An unconditionally energy stable finite difference scheme for a stochastic Cahn-Hilliard equation ⋮
High accuracy solutions to energy gradient flows from material science models ⋮
Mesh-robustness of an energy stable BDF2 scheme with variable steps for the Cahn-Hilliard model ⋮
Stabilized exponential-SAV schemes preserving energy dissipation law and maximum bound principle for the Allen-Cahn type equations ⋮
A fully discrete stable discontinuous Galerkin method for the thin film epitaxy problem without slope selection ⋮
A second order in time, uniquely solvable, unconditionally stable numerical scheme for Cahn-Hilliard-Navier-Stokes equation ⋮
Numerical solutions of the Allen-Cahn equation with the \(p\)-Laplacian ⋮
An accurate and parallel method with post-processing boundedness control for solving the anisotropic phase-field dendritic crystal growth model ⋮
Optimal rate convergence analysis of a second order scheme for a thin film model with slope selection ⋮
Unconditionally energy stable large time stepping method for the \(L^2\)-gradient flow based ternary phase-field model with precise nonlocal volume conservation ⋮
Numerical approximations for the molecular beam epitaxial growth model based on the invariant energy quadratization method ⋮
Preconditioned steepest descent methods for some nonlinear elliptic equations involving p-Laplacian terms ⋮
Error analysis of a decoupled, linear stabilization scheme for the Cahn-Hilliard model of two-phase incompressible flows
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