Numerical solution of convection–diffusion–reaction equations by a finite element method with error correlation
Sadia Akter Lima, Md. Kamrujjaman, Md. Shafiqul Islam
Abstract
This study contemplates the Finite Element Method (FEM), a well-known numerical method, to find numerical approximations of the Convection–Diffusion–Reaction (CDR) equation. We concentrate on analyzing the convergence and stability of the nonlinear parabolic partial equations. The method is generally applied without truncating the nonlinear terms and avoiding restrictive assumptions. Regular and irregular geometrical shapes are the key objective of this research paper. This study also focuses on the accuracy and acceptance of the FEM method by utilizing dissipation error, dispersion error, and total error analysis. The results are portrayed both graphically and in a tabular form, which virtually ensures the method’s validity and the algorithm’s efficiency to sustain the accuracy, simplicity, and applicability for solving nonlinear CDR equations. The proposed technique may also be applied for solving any nonlinear reaction–diffusion equations.