Convergence of finite volume schemes for a degenerate convection–diffusion equation arising in flow in porous media

2002 ◽  
Vol 191 (46) ◽  
pp. 5265-5286 ◽  
Author(s):  
M. Afif ◽  
B. Amaziane
Keyword(s):  
Porous Media ◽  
Diffusion Equation ◽  
Finite Volume ◽  
Flow In Porous Media ◽  
Finite Volume Schemes ◽  
Convection Diffusion ◽  
Convection Diffusion Equation

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.

scholarly journals A new formulation of finite difference and finite volume methods for solving a space fractional convection–diffusion model with fewer error estimates

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Reem Edwan ◽  
Shrideh Al-Omari ◽  
Mohammed Al-Smadi ◽  
Shaher Momani ◽  
Andreea Fulga
Keyword(s):  
Finite Difference ◽  
Finite Difference Method ◽  
Diffusion Equation ◽  
Finite Volume ◽  
Difference Method ◽  
Order Accuracy ◽  
Convection Diffusion ◽  
Convection Diffusion Equation ◽  
The Finite Difference Method ◽  
Volume Method

AbstractConvection and diffusion are two harmonious physical processes that transfer particles and physical quantities. This paper deals with a new aspect of solving the convection–diffusion equation in fractional order using the finite volume method and the finite difference method. In this context, we present an alternative way for estimating the space fractional derivative by utilizing the fractional Grünwald formula. The proposed methods are conditionally stable with second-order accuracy in space and first-order accuracy in time. Many comparisons are performed to display reliability and capability of the proposed methods. Furthermore, several results and conclusions are provided to indicate appropriateness of the finite volume method in solving the space fractional convection–diffusion equation compared with the finite difference method.

Sign in / Sign up

Export Citation Format

Share Document