A Uniquely Solvable, Energy Stable Numerical Scheme for the Functionalized Cahn–Hilliard Equation and Its Convergence Analysis

Convergence analysis and numerical implementation of a second order numerical scheme for the three-dimensional phase field crystal equation

(2018) Lixiu Dong et al.   COMPUTERS & MATHEMATICS WITH APPLICATIONS

A mass-conservative adaptive FAS multigrid solver for cell-centered finite difference methods on block-structured, locally-cartesian grids

(2018) Wenqiang Feng et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Preconditioned steepest descent methods for some nonlinear elliptic equations involving p-Laplacian terms

(2017) Wenqiang Feng et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Convergence analysis and error estimates for a second order accurate finite element method for the Cahn–Hilliard–Navier–Stokes system

(2017) Amanda E. Diegel et al.   NUMERISCHE MATHEMATIK

An $H^2$ convergence of a second-order convex-splitting, finite difference scheme for the three-dimensional Cahn–Hilliard equation

(2016) Jing Guo et al.   Communications in Mathematical Sciences

Efficient and stable exponential time differencing Runge–Kutta methods for phase field elastic bending energy models

(2016) Xiaoqiang Wang et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Analysis of Mixed Interior Penalty Discontinuous Galerkin Methods for the Cahn–Hilliard Equation and the Hele–Shaw Flow

(2016) Xiaobing Feng et al.   SIAM JOURNAL ON NUMERICAL ANALYSIS

Stability and convergence of a second-order mixed finite element method for the Cahn–Hilliard equation

(2015) Amanda E. Diegel et al.   IMA JOURNAL OF NUMERICAL ANALYSIS

Existence of pearled patterns in the planar functionalized Cahn–Hilliard equation

(2015) Keith Promislow et al.   JOURNAL OF DIFFERENTIAL EQUATIONS

Convergence analysis of a fully discrete finite difference scheme for the Cahn-Hilliard-Hele-Shaw equation

(2015) Wenbin Chen et al.   MATHEMATICS OF COMPUTATION

Analysis of a Mixed Finite Element Method for a Cahn--Hilliard--Darcy--Stokes System

(2015) Amanda E. Diegel et al.   SIAM JOURNAL ON NUMERICAL ANALYSIS

Analysis of symmetric interior penalty discontinuous Galerkin methods for the Allen–Cahn equation and the mean curvature flow

(2014) Xiaobing Feng et al.   IMA JOURNAL OF NUMERICAL ANALYSIS

Local Discontinuous Galerkin Methods for the Functionalized Cahn–Hilliard Equation

(2014) Ruihan Guo et al.   JOURNAL OF SCIENTIFIC COMPUTING

A Fourier pseudospectral method for the “good” Boussinesq equation with second-order temporal accuracy

(2014) Kelong Cheng et al.   NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS

Meander and Pearling of Single-Curvature Bilayer Interfaces in the Functionalized Cahn--Hilliard Equation

(2014) Arjen Doelman et al.   SIAM JOURNAL ON MATHEMATICAL ANALYSIS

A mixed discontinuous Galerkin, convex splitting scheme for a modified Cahn-Hilliard equation and an efficient nonlinear multigrid solver

(2013) Andreas C. Aristotelous et al.   DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B

Energy stable and efficient finite-difference nonlinear multigrid schemes for the modified phase field crystal equation

(2013) Arvind Baskaran et al.   JOURNAL OF COMPUTATIONAL PHYSICS

High accuracy solutions to energy gradient flows from material science models

(2013) Andrew Christlieb et al.   JOURNAL OF COMPUTATIONAL PHYSICS

A Linear Iteration Algorithm for a Second-Order Energy Stable Scheme for a Thin Film Model Without Slope Selection

(2013) Wenbin Chen et al.   JOURNAL OF SCIENTIFIC COMPUTING

Convergence Analysis of a Second Order Convex Splitting Scheme for the Modified Phase Field Crystal Equation

(2013) A. Baskaran et al.   SIAM JOURNAL ON NUMERICAL ANALYSIS

Efficient spectral-Galerkin methods for systems of coupled second-order equations and their applications

(2012) Feng Chen et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Second-order Convex Splitting Schemes for Gradient Flows with Ehrlich–Schwoebel Type Energy: Application to Thin Film Epitaxy

(2012) Jie Shen et al.   SIAM JOURNAL ON NUMERICAL ANALYSIS

Variational Models of Network Formation and Ion Transport: Applications to Perfluorosulfonate Ionomer Membranes

(2012) Nir Gavish et al.   Polymers

A Linear Energy Stable Scheme for a Thin Film Model Without Slope Selection

(2011) Wenbin Chen et al.   JOURNAL OF SCIENTIFIC COMPUTING

An Energy Stable and Convergent Finite-Difference Scheme for the Modified Phase Field Crystal Equation

(2011) C. Wang et al.   SIAM JOURNAL ON NUMERICAL ANALYSIS

Unconditionally stable schemes for equations of thin film epitaxy

(2010) Steven Wise et al.   DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS

Curvature driven flow of bi-layer interfaces

(2010) Nir Gavish et al.   PHYSICA D-NONLINEAR PHENOMENA

Stable and efficient finite-difference nonlinear-multigrid schemes for the phase field crystal equation

(2009) Z. Hu et al.   JOURNAL OF COMPUTATIONAL PHYSICS

A new phase-field model for strongly anisotropic systems

(2009) S. Torabi et al.   PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES

PEM Fuel Cells: A Mathematical Overview

(2009) Keith Promislow et al.   SIAM JOURNAL ON APPLIED MATHEMATICS

An Energy-Stable and Convergent Finite-Difference Scheme for the Phase Field Crystal Equation

(2009) S. M. Wise et al.   SIAM JOURNAL ON NUMERICAL ANALYSIS