A SCR-based error estimation and adaptive finite element method for the Allen-Cahn equation
DOI10.1016/j.camwa.2019.02.022zbMath1442.65253OpenAlexW2918504611MaRDI QIDQ2204063
Yunqing Huang, Yaoyao Chen, Nian-Yu Yi
Publication date: 2 October 2020
Published in: Computers \& Mathematics with Applications (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.camwa.2019.02.022
finite element methoda posteriori error estimationAllen-Cahn equationadaptivesuperconvergent cluster recovery
Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Error bounds for initial value and initial-boundary value problems involving PDEs (65M15) Mesh generation, refinement, and adaptive methods for the numerical solution of initial value and initial-boundary value problems involving PDEs (65M50) Dynamic and nonequilibrium phase transitions (general) in statistical mechanics (82C26)
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Cites Work
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- Numerical methods for solving the Cahn-Hilliard equation and its applicability to related energy-based models
- On the maximum principle preserving schemes for the generalized Allen-Cahn equation
- Nonlinear stability of the implicit-explicit methods for the Allen-Cahn equation
- Recovery of normal derivatives from the piecewise \(L^2\) projection
- On second order semi-implicit Fourier spectral methods for 2D Cahn-Hilliard equations
- Numerical simulation of the three dimensional Allen-Cahn equation by the high-order compact ADI method
- An unconditionally stable hybrid numerical method for solving the Allen-Cahn equation
- The superconvergent cluster recovery method
- Multiphase image segmentation using a phase-field model
- Numerical approximations of Allen-Cahn and Cahn-Hilliard equations
- Modeling and computation of two phase geometric biomembranes using surface finite elements
- Numerical analysis of the Allen-Cahn equation and approximation for mean curvature flows
- A continuum model of grain boundaries
- A second order operator splitting method for Allen-Cahn type equations with nonlinear source terms
- 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
- A phase field concept for multiphase systems
- The stabilized semi-implicit finite element method for the surface Allen-Cahn equation
- Second order schemes and time-step adaptivity for Allen-Cahn and Cahn-Hilliard models
- A semi-analytical Fourier spectral method for the Allen-Cahn equation
- An unconditionally energy stable second order finite element method for solving the Allen-Cahn equation
- Threshold dynamics for the piecewise constant Mumford-Shah functional
- A posteriori error estimates and an adaptive finite element method for the Allen-Cahn equation and the mean curvature flow
- Robust A Priori and A Posteriori Error Analysis for the Approximation of Allen–Cahn and Ginzburg–Landau Equations Past Topological Changes
- Analysis of symmetric interior penalty discontinuous Galerkin methods for the Allen–Cahn equation and the mean curvature flow
- Numerical Studies of Discrete Approximations to the Allen–Cahn Equation in the Sharp Interface Limit
- Numerical Analysis of a Continuum Model of Phase Transition
- The superconvergent patch recovery anda posteriori error estimates. Part 2: Error estimates and adaptivity
- Higher Order Local Accuracy by Averaging in the Finite Element Method
- A Second-Order Convex Splitting Scheme for a Cahn-Hilliard Equation with Variable Interfacial Parameters
- SharpL2-Error Estimates and Superconvergence of Mixed Finite Element Methods for Non-Fickian Flows in Porous Media
- Quantitative phase-field modeling of dendritic growth in two and three dimensions
- Some Weighted Averaging Methods for Gradient Recovery
- A posteriorierror control for the Allen–Cahn problem: circumventing Gronwall's inequality
- A New Finite Element Gradient Recovery Method: Superconvergence Property
- Color Image Segmentation by the Vector-Valued Allen–Cahn Phase-Field Model: A Multigrid Solution
- Interface Dynamics and Far-From-Equilibrium Phase Transitions in Multilayer Epitaxial Growth and Erosion on Crystal Surfaces: Continuum Theory Insights
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