Fractional spectral vanishing viscosity method: application to the quasi-geostrophic equation

DOI10.1016/j.chaos.2017.03.052zbMath1422.65289OpenAlexW2605484989MaRDI QIDQ1677786

Fangying Song, George Em. Karniadakis

Publication date: 13 November 2017

Published in: Chaos, Solitons and Fractals (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.chaos.2017.03.052

zbMATH Keywords

spectral element methodsingular solutionsfractional conservations laws

Mathematics Subject Classification ID

Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Meteorology and atmospheric physics (86A10) Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs (65M70) PDEs in connection with geophysics (35Q86)

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Cites Work

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• A two-grid finite element approximation for a nonlinear time-fractional Cable equation
• A generalization of the Hopf-Cole transformation
• New numerical results for the surface quasi-geostrophic equation
• Stabilized spectral element computations of high Reynolds number incompressible flows
• A spectral element method for fluid dynamics: Laminar flow in a channel expansion
• Spectral element simulations of laminar and turbulent flows in complex geometries
• A spectral vanishing viscosity method for large eddy simulations
• High-order algorithms for large eddy simulation of incompressible flows
• Fractional Burgers equation with nonlinear non-locality: spectral vanishing viscosity and local discontinuous Galerkin methods
• Nonsingular surface quasi-geostrophic flow
• Finite difference/finite element method for a nonlinear time-fractional fourth-order reaction-diffusion problem
• Finite difference/spectral approximations for the time-fractional diffusion equation
• Convergence of Spectral Methods for Nonlinear Conservation Laws
• Formation of strong fronts in the 2-D quasigeostrophic thermal active scalar
• Legendre Pseudospectral Viscosity Method for Nonlinear Conservation Laws
• Behavior of Solutions of 2D Quasi-Geostrophic Equations
• Surface quasi-geostrophic dynamics
• Computing Fractional Laplacians on Complex-Geometry Domains: Algorithms and Simulations
• Inviscid and inviscid-limit behavior of a surface quasigeostrophic flow