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Comparative Study of Finite Difference and Finite Element Methods for Solving 2D Parabolic Convection–Diffusion–Reaction Equations With Variable Coefficients

Sparad:
I publikationen:International Journal of Differential Equations vol. 2025, no. 1 (2025)
Huvudupphov: Tsega, Endalew Getnet
Utgiven:
John Wiley & Sons, Inc.
Ämnen:
Accuracy
Comparative studies
Finite element method
Finite volume method
Behavior
Convection
Mathematical analysis
Quadratures
Finite difference method
Chemical reactions
Time integration
Reaction-diffusion equations
Numerical analysis
Engineering
Boundary conditions
Discretization
Efficiency
Diffusion coefficient
Contamination
Länkar:Citation/Abstract
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Abstrakt:This study investigates the numerical solution of two‐dimensional parabolic convection–diffusion–reaction (CDR) equations with variable coefficients using the finite difference method (FDM) and the finite element method (FEM). The FDM employs central differences for spatial discretization and the implicit Euler method for time integration, while the FEM uses the Galerkin approach with rectangular elements and three‐point Gauss–Legendre quadrature for spatial integrals, followed by implicit Euler discretization in time. Three test problems are considered to compare accuracy and efficiency. For small diffusion coefficients, the FEM provides higher accuracy, whereas for larger diffusion coefficients, both methods deliver nearly identical accuracy. Despite its improved accuracy in certain cases, the FEM typically involves a higher computational cost than the FDM. Based on the results, the study recommends the use of FEM for problems with boundary or interior layers.
ISSN:1687-9643
1687-9651
DOI:10.1155/ijde/2126609
Källa:Advanced Technologies & Aerospace Database