Numerical analysis of a second-order IPDGFE method for the Allen-Cahn equation and the curvature-driven geometric flow

DOI10.1016/j.camwa.2021.01.014OpenAlexW3131933093WikidataQ112880451 ScholiaQ112880451MaRDI QIDQ1999224

Junzhao Hu, Huanrong Li, Zhengyuan Song

Publication date: 18 March 2021

Published in: Computers \& Mathematics with Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.camwa.2021.01.014

zbMATH Keywords

error estimatesAllen-Cahn equationinterior penalty discontinuous Galerkin methodmodified Crank-Nicolson schemecurvature-driven geometric flow

Mathematics Subject Classification ID

PDEs in connection with fluid mechanics (35Q35) 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) 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)

Related Items (13)

Numerical analysis of energy-stable Crank-Nicolson finite difference schemes for the phase-field equation ⋮ A reduced-order characteristic finite element method based on POD for optimal control problem governed by convection-diffusion equation ⋮ Reduced‐order extrapolation technique for coefficient vectors of numerical solutions about fluid mechanics equation ⋮ Effective time step analysis for the Allen–Cahn equation with a high‐order polynomial free energy ⋮ 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 ⋮ A reduced-order Schwarz domain decomposition method based on POD for the convection-diffusion equation ⋮ Adaptive discontinuous Galerkin finite element methods for the Allen-Cahn equation on polygonal meshes ⋮ 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 conservative Allen-Cahn equation with a curvature-dependent Lagrange multiplier ⋮ An explicit stable finite difference method for the Allen-Cahn equation ⋮ Operator splitting scheme based on barycentric Lagrange interpolation collocation method for the Allen-Cahn equation

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