A higher order richardson scheme for a singularly perturbed semilinear elliptic convection-diffusion equation

2010 ◽  
Vol 50 (3) ◽  
pp. 437-456 ◽  
Author(s):  
G. I. Shishkin ◽  
L. P. Shishkina
Keyword(s):  
Diffusion Equation ◽  
Higher Order ◽  
Singularly Perturbed ◽  
Convection Diffusion ◽  
Convection Diffusion Equation ◽  
Semilinear Elliptic

scholarly journals On Convergence of the Exponentially Fitted Finite Volume Method With an Anisotropic Mesh Refinement for a Singularly Perturbed Convection-diffusion Equation

2003 ◽  
Vol 3 (3) ◽  
pp. 493-512 ◽  
Author(s):  
Song Wang ◽  
Lutz Angermann
Keyword(s):  
Diffusion Equation ◽  
Finite Volume Method ◽  
Finite Volume ◽  
Two Dimensions ◽  
Singularly Perturbed ◽  
Discrete Energy ◽  
Convection Diffusion ◽  
Convection Diffusion Equation ◽  
Exponentially Fitted ◽  
Volume Method

AbstractThis paper presents a convergence analysis for the exponentially fitted finite volume method in two dimensions applied to a linear singularly perturbed convection-diffusion equation with exponential boundary layers. The method is formulated as a nonconforming Petrov-Galerkin finite element method with an exponentially fitted trial space and a piecewise constant test space. The corresponding bilinear form is proved to be coercive with respect to a discrete energy norm. Numerical results are presented to verify the theoretical rates of convergence.

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