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

R. Soundararajan, V. Subburayan () and Patricia J. Y. Wong
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R. Soundararajan: Department of Mathematics, RKM Vivekananda College (Autonomous), Mylapore, Chennai 600004, India
V. Subburayan: Department of Mathematics, Faculty of Engineering and Technology, SRM Institute of Science and Technology, Kattankulathur 603203, India
Patricia J. Y. Wong: School of Electrical and Electronic Engineering, Nanyang Technological University, 50 Nanyang Avenue, Singapore 639798, Singapore

Mathematics, 2023, vol. 11, issue 9, 1-17

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

Keywords: singularly perturbed problem; parabolic differential equation; convection–diffusion problem; line discontinuous source term; streamline–diffusion finite element method; Shishkin mesh; uniformly convergent (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
References: View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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