A modified finite volume element method for solving the phase field Allen-Cahn model

DOI10.1016/J.AML.2021.107860OpenAlexW4200460687MaRDI QIDQ2077042

Dongmei Wang, Huanrong Li

Publication date: 22 February 2022

Published in: Applied Mathematics Letters (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.aml.2021.107860

zbMATH Keywords

error estimatesproper orthogonal decompositionAllen-Cahn modelmodified finite volume element method

Mathematics Subject Classification ID

Finite difference methods applied to problems in fluid mechanics (76M20) 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) Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems (65M99) Finite volume methods for initial value and initial-boundary value problems involving PDEs (65M08)

Related Items (5)

Numerical analysis of energy-stable Crank-Nicolson finite difference schemes for the phase-field equation ⋮ Unconditionally energy-stable time-marching methods for the multi-phase conservative Allen-Cahn fluid models based on a modified SAV approach ⋮ Local radial basis function collocation method preserving maximum and monotonicity principles for nonlinear differential equations ⋮ Analysis of two spectral Galerkin approximation schemes for solving the perturbed FitzHugh-Nagumo neuron model ⋮ A modified Crank-Nicolson finite difference method preserving maximum-principle for the phase-field model

Cites Work

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• Error estimate of the finite volume scheme for the Allen-Cahn equation
• A reduced-order finite element method based on proper orthogonal decomposition for the Allen-Cahn model
• Numerical analysis of an unconditionally energy-stable reduced-order finite element method for the Allen-Cahn phase field model
• A highly efficient reduced-order extrapolated finite difference algorithm for time-space tempered fractional diffusion-wave equation
• An optimizing implicit difference scheme based on proper orthogonal decomposition for the two-dimensional unsaturated soil water flow equation
• Finite Element Methods for the Stochastic Allen--Cahn Equation with Gradient-type Multiplicative Noise

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