Asymptotically Compatible Fourier Spectral Approximations of Nonlocal Allen--Cahn Equations

DOI10.1137/15M1039857zbMath1342.65198MaRDI QIDQ5739959

Jiang Yang, Qiang Du

Publication date: 7 July 2016

Published in: SIAM Journal on Numerical Analysis (Search for Journal in Brave)

zbMATH Keywords

convergencenumerical exampleerror estimatesnonlocal modelsFourier spectral methodsasymptotically compatible schemesnonlocal Allen-Cahn equations

Mathematics Subject Classification ID

PDEs in connection with fluid mechanics (35Q35) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs (65M70) Error bounds for initial value and initial-boundary value problems involving PDEs (65M15)

Related Items (39)

Numerical methods for nonlocal and fractional models ⋮ A high order operator splitting method based on spectral deferred correction for the nonlocal viscous Cahn-Hilliard equation ⋮ Energy-decreasing exponential time differencing Runge-Kutta methods for phase-field models ⋮ Second-order maximum principle preserving Strang's splitting schemes for anisotropic fractional Allen-Cahn equations ⋮ A general and fast convolution-based method for peridynamics: applications to elasticity and brittle fracture ⋮ An optimization-based approach to parameter learning for fractional type nonlocal models ⋮ Stabilized linear semi-implicit schemes for the nonlocal Cahn-Hilliard equation ⋮ Asymptotic Analysis on the Sharp Interface Limit of the Time-Fractional Cahn--Hilliard Equation ⋮ Efficient, linear and fast numerical algorithm for the volume conserved nonlocal Allen-Cahn equation ⋮ A dimensional splitting exponential time differencing scheme for multidimensional fractional Allen-Cahn equations ⋮ Asymptotically compatible schemes for space-time nonlocal diffusion equations ⋮ Numerical analysis of fully discretized Crank-Nicolson scheme for fractional-in-space Allen-Cahn equations ⋮ A two‐grid finite element method for the Allen‐Cahn equation with the logarithmic potential ⋮ High-order unconditionally maximum-principle-preserving parametric integrating factor Runge-Kutta schemes for the nonlocal Allen-Cahn equation ⋮ Analytical and numerical dissipativity for the space-fractional Allen-Cahn equation ⋮ Nonlocal effects on a 1D generalized Ohta-Kawasaki model ⋮ Mathematics of smoothed particle hydrodynamics: a study via nonlocal Stokes equations ⋮ Double stabilizations and convergence analysis of a second-order linear numerical scheme for the nonlocal Cahn-Hilliard equation ⋮ Regularity of solutions for nonlocal diffusion equations on periodic distributions ⋮ A Fast Implementation of the Linear Bond-Based Peridynamic Beam Model ⋮ Convergence analysis for a stabilized linear semi-implicit numerical scheme for the nonlocal Cahn–Hilliard equation ⋮ Time-fractional Allen-Cahn equations: analysis and numerical methods ⋮ Maximum Principle Preserving Exponential Time Differencing Schemes for the Nonlocal Allen--Cahn Equation ⋮ Asymptotically Compatible Reproducing Kernel Collocation and Meshfree Integration for Nonlocal Diffusion ⋮ Fourier multipliers for nonlocal Laplace operators ⋮ Fast and accurate implementation of Fourier spectral approximations of nonlocal diffusion operators and its applications ⋮ Analysis of fully discrete approximations for dissipative systems and application to time-dependent nonlocal diffusion problems ⋮ A spectral method for nonlocal diffusion operators on the sphere ⋮ A fast convolution-based method for peridynamic transient diffusion in arbitrary domains ⋮ A discontinuous Galerkin method for one-dimensional time-dependent nonlocal diffusion problems ⋮ A spectral collocation method for nonlocal diffusion equations with volume constrained boundary conditions ⋮ A discontinuous Galerkin method with penalty for one-dimensional nonlocal diffusion problems ⋮ Local discontinuous Galerkin scheme for space fractional Allen-Cahn equation ⋮ Asymptotically Compatible Schemes for Robust Discretization of Parametrized Problems with Applications to Nonlocal Models ⋮ Higher order collocation methods for nonlocal problems and their asymptotic compatibility ⋮ Robust a posteriori stress analysis for quadrature collocation approximations of nonlocal models via nonlocal gradients ⋮ Fast algorithm for nonlocal Allen-Cahn equation with scalar auxiliary variable approach ⋮ On a nonlocal Cahn–Hilliard model permitting sharp interfaces ⋮ New Insights on Convergence Properties of Peridynamic Models for Transient Diffusion and Elastodynamics

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