An operator splitting method with FDM and FEM for the convection- diffusion equation using boundary-fitted coordinate system

1996 ◽  
Vol 1 (4) ◽  
pp. 55-58
Author(s):  
Jie-Min Zhan ◽  
Yao-Song Chen
Keyword(s):  
Diffusion Equation ◽  
Coordinate System ◽  
Operator Splitting ◽  
Splitting Method ◽  
Convection Diffusion ◽  
Convection Diffusion Equation ◽  
Operator Splitting Method

scholarly journals Entropy Schemes for One-Dimensional Convection-Diffusion Equations

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-5
Author(s):  
Rongsan Chen
Keyword(s):  
Diffusion Equation ◽  
Hyperbolic Conservation Laws ◽  
Operator Splitting ◽  
Splitting Method ◽  
Order Accuracy ◽  
Central Difference ◽  
One Dimensional ◽  
Convection Diffusion ◽  
Convection Diffusion Equation ◽  
Operator Splitting Method

In this paper, we extend the entropy scheme for hyperbolic conservation laws to one-dimensional convection-diffusion equation. The operator splitting method is used to solve the convection-diffusion equation that is divided into conservation and diffusion parts, in which the first-order accurate entropy scheme is applied to solve the conservation part and the second accurate central difference scheme is applied to solve the diffusion part. Numerical tests show that the L∞ error achieves about second-order accuracy, but the L1 error reaches about forth-order accuracy.

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