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Development and Error Analysis of a Novel FEM for Convection–Diffusion–Reaction Equations | ||
| Computational Methods for Differential Equations | ||
| مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 24 مرداد 1405 اصل مقاله (1.57 M) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22034/cmde.2026.69000.3384 | ||
| نویسندگان | ||
| Sadia Akter Lima1؛ Md Shafiqul Islam2؛ Runchang Lin3؛ Md Kamrujjaman* 4 | ||
| 1Department of Applied Mathematics, Noakhali Science and Technology University, Noakhali 3814, Bangladesh. | ||
| 2Department of Applied Mathematics, University of Dhaka, Dhaka 1000, Bangladesh. | ||
| 3Department of Mathematics and Physics, Texas A&M International University, TX 78041, USA. | ||
| 4Department of Mathematics, University of Dhaka, Dhaka 1000, Bangladesh. | ||
| چکیده | ||
| This study examines the Finite Element Method (FEM) as an effective numerical approach for solving two-dimensional (2D) higher-order, non-homogeneous, and non-linear convection-diffusion-reaction (CDR) equations. A key focus is on convergence and stability analysis for non-linear parabolic partial differential equations (PDEs) and the CDR model. Unlike conventional methods that simplify non-linearity through assumptions, our approach retains the full complexity of the equations, demonstrating FEM’s robustness and versatility. We apply FEM to unsteady-state problems, emphasizing its accuracy and computational efficiency. Various error analyses validate the method’s reliability. To further assess its performance, we conduct extensive numerical experiments, with graphical representations reinforcing the accuracy and stability of FEM in solving spatially distributed 2D CDR equations. The results establish FEM as a powerful and reliable tool for solving non-linear PDEs while maintaining computational stability and practical applicability. Its ability to handle intricate non-linear dynamics without restrictive assumptions highlights its potential in real-world applications. The study affirms that FEM is not only efficient but also a versatile numerical technique for solving complex 2D parabolic PDEs and CDR models, making it a valuable asset in scientific and engineering computations. | ||
| کلیدواژهها | ||
| Non-linear PDE؛ finite element method؛ CDR equation؛ error analysis | ||
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آمار تعداد مشاهده مقاله: 39 تعداد دریافت فایل اصل مقاله: 62 |
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