Streamline Diffusion Finite Element Method for Singularly Perturbed 1D-Parabolic Convection Diffusion Differential Equations with Line Discontinuous Source

This article presents a study on singularly perturbed 1D parabolic Dirichlet’s type differential equations with discontinuous source terms an interior line. The time derivative is discretized using the Euler backward method, followed by application of streamline–diffusion finite element method (SDFEM) to solve locally one-dimensional stationary problems Shishkin mesh. Our proposed shown achieve first-order convergence in and second-order space. offers several advantages over existing techniques, including more accurate approximations solution boundary layer region, better efficiency, robustness dealing line terms. numerical examples presented this paper demonstrate effectiveness efficiency our which has practical applications various fields, such as engineering applied mathematics. Overall, provides effective efficient challenging problem solving terms, making it valuable tool for researchers practitioners domains.