The BDF3/EP3 scheme for MBE with no slope selection is stable

DOI10.1007/s10915-021-01642-5OpenAlexW3204782967MaRDI QIDQ2233971

Yanyan Li

Publication date: 12 October 2021

Published in: Journal of Scientific Computing (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2106.08041

zbMATH Keywords

phase field modelmolecular beam epitaxyenergy stabilityno slope selection

Mathematics Subject Classification ID

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) Extrapolation to the limit, deferred corrections (65B05) Statistical mechanics of semiconductors (82D37) Error bounds for initial value and initial-boundary value problems involving PDEs (65M15)

Related Items (8)

A new class of implicit-explicit BDF\(k\) SAV schemes for general dissipative systems and their error analysis ⋮ Energy stability of BDF methods up to fifth-order for the molecular beam epitaxial model without slope selection ⋮ A family of structure-preserving exponential time differencing Runge-Kutta schemes for the viscous Cahn-Hilliard equation ⋮ An energy stable linear BDF2 scheme with variable time-steps for the molecular beam epitaxial model without slope selection ⋮ A new third-order energy stable technique and error estimate for the extended Fisher-Kolmogorov equation ⋮ Energy stable and convergent BDF3-5 schemes for the molecular beam epitaxial model with slope selection ⋮ Two energy stable variable-step L1 schemes for the time-fractional MBE model without slope selection ⋮ On the Cahn-Hilliard-Brinkman Equations in $\mathbb{R}^4$: Global Well-Posedness

Cites Work

• On second order semi-implicit Fourier spectral methods for 2D Cahn-Hilliard equations
• Numerical approximations of Allen-Cahn and Cahn-Hilliard equations
• Gradient bounds for a thin film epitaxy equation
• Unconditionally stable schemes for equations of thin film epitaxy
• 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
• On the stabilization size of semi-implicit Fourier-spectral methods for 3D Cahn-Hilliard equations
• A linear energy stable scheme for a thin film model without slope selection
• An improved gradient bound for 2D MBE
• Characterizing the Stabilization Size for Semi-Implicit Fourier-Spectral Method to Phase Field Equations
• Second-order Convex Splitting Schemes for Gradient Flows with Ehrlich–Schwoebel Type Energy: Application to Thin Film Epitaxy
• Convergence of an Embedded Exponential-Type Low-Regularity Integrators for the KdV Equation without Loss of Regularity
• A First Course in the Numerical Analysis of Differential Equations
• The stability properties ofq-step backward difference schemes
• A-BDF: A Generalization of the Backward Differentiation Formulae
• An Introduction to Numerical Analysis
• Thin film epitaxy with or without slope selection
• A Third Order BDF Energy Stable Linear Scheme for the No-Slope-Selection Thin Film Model
• A New Class of Efficient and Robust Energy Stable Schemes for Gradient Flows
• On the instability of high order backward-difference multistep methods
• A special stability problem for linear multistep methods
• Stability Analysis of Large Time‐Stepping Methods for Epitaxial Growth Models

This page was built for publication: The BDF3/EP3 scheme for MBE with no slope selection is stable