The Evolution of Finite Element Approaches in Reaction-Diffusion Modeling

R Sharma, OP Yadav - Archives of Computational Methods in Engineering, 2025 - Springer
This paper presents a comprehensive review of finite element methods (FEMs) applied to a
diverse range of reaction-diffusion equations (RDEs). Beginning with a historical overview of …

A robust weak Galerkin finite element method for two parameter singularly perturbed parabolic problems on nonuniform meshes

J Singh, N Kumar, R Jiwari - Journal of Computational Science, 2024 - Elsevier
In this study, we proposed a weak Galerkin finite element method (WG-FEM) for solving two-
parameter singularly perturbed parabolic problems (TP-SPPPs) of convection–diffusion …

Numerical Analysis of Stabilizer‐Free Weak Galerkin Finite Element Method for Time‐Dependent Differential Equation Under Low Regularity

X Liu, Y Zou, Y Wang, C Zhou… - Numerical Methods for …, 2025 - Wiley Online Library
In this article, we focus on investigating the optimal convergence order of error estimates for
the stabilizer‐free weak Galerkin finite element method for a second‐order time‐dependent …

A Crank-Nicolson WG-FEM for unsteady 2D convection-diffusion equation with nonlinear reaction term on layer adapted mesh

N Kumar, S Toprakseven, NS Yadav… - Applied Numerical …, 2024 - Elsevier
This paper is contributed to explore how a Crank-Nicolson weak Galerkin finite element
method (WG-FEM) addresses the singularly perturbed unsteady convection-diffusion …

Application of Fixed Point Theory and Solitary Wave Solutions for the Time-Fractional Nonlinear Unsteady Convection-Diffusion System

M Shahzad, N Ahmed, MS Iqbal, M Inc… - International Journal of …, 2023 - Springer
In this article, the two-dimensional time fractional unsteady convection-diffusion system is
under consideration. The convection-diffusion system of nonlinear partial differential …