An optimal error estimate for the two-dimensional nonlinear time fractional advection-diffusion equation with smooth and non-smooth solutions

DOI10.1016/j.camwa.2019.12.013zbMath1447.65096OpenAlexW2997259235WikidataQ126471915 ScholiaQ126471915MaRDI QIDQ2192468

Junqing Jia, Hui Zhang, Xiao-yun Jiang

Publication date: 17 August 2020

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

Full work available at URL: https://doi.org/10.1016/j.camwa.2019.12.013

zbMATH Keywords

correction methodoptimal error estimateerror splitting argument techniquelinearized \(L1\) Legendre-Galerkin spectral methodtwo-dimensional nonlinear time fractional advection-diffusion equation

Mathematics Subject Classification ID

Spectral, collocation and related methods for boundary value problems involving PDEs (65N35) Fractional derivatives and integrals (26A33) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) 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) 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) Fractional partial differential equations (35R11) Numerical solution of discretized equations for initial value and initial-boundary value problems involving PDEs (65M22)

Related Items (6)

Local discontinuous Galerkin method based on a family of second-order time approximation schemes for fractional mobile/immobile convection-diffusion equations ⋮ Fast method and convergence analysis for the magnetohydrodynamic flow and heat transfer of fractional Maxwell fluid ⋮ Global superconvergence analysis of nonconforming finite element method for time fractional reaction-diffusion problem with anisotropic data ⋮ A novel meshless method based on RBF for solving variable-order time fractional advection-diffusion-reaction equation in linear or nonlinear systems ⋮ Unsteady natural convection boundary layer flow and heat transfer past a vertical flat plate with novel constitution models ⋮ Fast high-order difference scheme for the modified anomalous subdiffusion equation based on fast discrete sine transform

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