scholarly journals Optimal error estimate of the Legendre spectral approximation for space-fractional reaction–advection–diffusion equation

2018 ◽  
Vol 2018 (1) ◽  
Author(s):  
Wenping Chen ◽  
Shujuan Lü ◽  
Hu Chen ◽  
Haiyu Liu
Keyword(s):  
Diffusion Equation ◽  
Error Estimate ◽  
Optimal Error Estimate ◽  
Spectral Approximation ◽  
Optimal Error ◽  
Advection Diffusion Equation ◽  
Advection Diffusion ◽  
Fractional Reaction

FRACTIONAL STEP METHODS FOR SPECTRAL APPROXIMATION OF ADVECTION-DIFFUSION EQUATIONS

1996 ◽  
Vol 06 (07) ◽  
pp. 1027-1050 ◽  
Author(s):  
PAOLA GERVASIO
Keyword(s):  
Diffusion Equation ◽  
Boundary Conditions ◽  
Peclet Number ◽  
Diffusion Equations ◽  
Fractional Step ◽  
Spectral Approximation ◽  
Two Dimensional ◽  
Advection Diffusion Equation ◽  
Advection Diffusion ◽  
Large Peclet Number

Several classical fractional step schemes are proposed for the spectral approximation of advection-diffusion equation in two-dimensional geometries. Suitable boundary conditions are studied in order to preserve the accuracy of the schemes at each step. An example is given for the application of the fractional step schemes to solve problems with large Péclet number.

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