A Powerful High-Order B-Spline Galerkin Technique for Numerical Solutions of Advection-Diffusion Equation

Azhar Iqbal; Tayyaba Akram; Waseem Ahmad Khan; Ajmal Ali

doi:10.1007/978-981-97-2089-7_6

A Powerful High-Order B-Spline Galerkin Technique for Numerical Solutions of Advection-Diffusion Equation

Azhar Iqbal^*
, Tayyaba Akram
, Waseem Ahmad Khan
, Ajmal Ali

^*Corresponding author for this work

Department of Mathematics

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

Abstract

The present paper proposes a novel numerical approach for solving the advection-diffusion equation using quintic B-spline functions combined with the Galerkin finite element method. The advection-diffusion equation is a fundamental partial differential equation that is used in a variety of scientific and engineering domains, including fluid dynamics, heat transfer, and environmental modeling. The finite difference scheme is applied for time derivative, and Crank-Nicolson scheme is used for space parameters. The proposed approach, which is found to be accurate and effective, is validated with two numerical problems. The numerical results indicate that the present scheme performs well and correctly with the higher-order B-spline functions. To see the performance of the method, the error norms and are measured.

Original language	English
Title of host publication	Soft Computing
Subtitle of host publication	Theories and Applications - Proceedings of SoCTA 2023
Editors	Rajesh Kumar, Ajit Kumar Verma, Om Prakash Verma, Tanu Wadehra
Publisher	Springer Science and Business Media Deutschland GmbH
Pages	59-68
Number of pages	10
ISBN (Print)	9789819720880
DOIs	https://doi.org/10.1007/978-981-97-2089-7_6
State	Published - 2024
Event	7th International Conference on Soft Computing: Theories and Applications, SoCTA 2023 - Una, India Duration: 21 Dec 2023 → 23 Dec 2023

Publication series

Name	Lecture Notes in Networks and Systems
Volume	971 LNNS
ISSN (Print)	2367-3370
ISSN (Electronic)	2367-3389

Conference

Conference	7th International Conference on Soft Computing: Theories and Applications, SoCTA 2023
Country/Territory	India
City	Una
Period	21/12/23 → 23/12/23

Bibliographical note

Publisher Copyright:
© The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2024.

Keywords

Advection-diffusion
Finite element method
High-order B-spline functions

ASJC Scopus subject areas

Control and Systems Engineering
Signal Processing
Computer Networks and Communications

Access to Document

10.1007/978-981-97-2089-7_6

Cite this

Iqbal, A., Akram, T., Khan, W. A., & Ali, A. (2024). A Powerful High-Order B-Spline Galerkin Technique for Numerical Solutions of Advection-Diffusion Equation. In R. Kumar, A. K. Verma, O. P. Verma, & T. Wadehra (Eds.), Soft Computing: Theories and Applications - Proceedings of SoCTA 2023 (pp. 59-68). (Lecture Notes in Networks and Systems; Vol. 971 LNNS). Springer Science and Business Media Deutschland GmbH. https://doi.org/10.1007/978-981-97-2089-7_6

Iqbal, Azhar ; Akram, Tayyaba ; Khan, Waseem Ahmad et al. / A Powerful High-Order B-Spline Galerkin Technique for Numerical Solutions of Advection-Diffusion Equation. Soft Computing: Theories and Applications - Proceedings of SoCTA 2023. editor / Rajesh Kumar ; Ajit Kumar Verma ; Om Prakash Verma ; Tanu Wadehra. Springer Science and Business Media Deutschland GmbH, 2024. pp. 59-68 (Lecture Notes in Networks and Systems).

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abstract = "The present paper proposes a novel numerical approach for solving the advection-diffusion equation using quintic B-spline functions combined with the Galerkin finite element method. The advection-diffusion equation is a fundamental partial differential equation that is used in a variety of scientific and engineering domains, including fluid dynamics, heat transfer, and environmental modeling. The finite difference scheme is applied for time derivative, and Crank-Nicolson scheme is used for space parameters. The proposed approach, which is found to be accurate and effective, is validated with two numerical problems. The numerical results indicate that the present scheme performs well and correctly with the higher-order B-spline functions. To see the performance of the method, the error norms and are measured.",

keywords = "Advection-diffusion, Finite element method, High-order B-spline functions",

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Iqbal, A, Akram, T, Khan, WA & Ali, A 2024, A Powerful High-Order B-Spline Galerkin Technique for Numerical Solutions of Advection-Diffusion Equation. in R Kumar, AK Verma, OP Verma & T Wadehra (eds), Soft Computing: Theories and Applications - Proceedings of SoCTA 2023. Lecture Notes in Networks and Systems, vol. 971 LNNS, Springer Science and Business Media Deutschland GmbH, pp. 59-68, 7th International Conference on Soft Computing: Theories and Applications, SoCTA 2023, Una, India, 21/12/23. https://doi.org/10.1007/978-981-97-2089-7_6

A Powerful High-Order B-Spline Galerkin Technique for Numerical Solutions of Advection-Diffusion Equation. / Iqbal, Azhar; Akram, Tayyaba; Khan, Waseem Ahmad et al.
Soft Computing: Theories and Applications - Proceedings of SoCTA 2023. ed. / Rajesh Kumar; Ajit Kumar Verma; Om Prakash Verma; Tanu Wadehra. Springer Science and Business Media Deutschland GmbH, 2024. p. 59-68 (Lecture Notes in Networks and Systems; Vol. 971 LNNS).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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AB - The present paper proposes a novel numerical approach for solving the advection-diffusion equation using quintic B-spline functions combined with the Galerkin finite element method. The advection-diffusion equation is a fundamental partial differential equation that is used in a variety of scientific and engineering domains, including fluid dynamics, heat transfer, and environmental modeling. The finite difference scheme is applied for time derivative, and Crank-Nicolson scheme is used for space parameters. The proposed approach, which is found to be accurate and effective, is validated with two numerical problems. The numerical results indicate that the present scheme performs well and correctly with the higher-order B-spline functions. To see the performance of the method, the error norms and are measured.

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Iqbal A, Akram T, Khan WA, Ali A. A Powerful High-Order B-Spline Galerkin Technique for Numerical Solutions of Advection-Diffusion Equation. In Kumar R, Verma AK, Verma OP, Wadehra T, editors, Soft Computing: Theories and Applications - Proceedings of SoCTA 2023. Springer Science and Business Media Deutschland GmbH. 2024. p. 59-68. (Lecture Notes in Networks and Systems). doi: 10.1007/978-981-97-2089-7_6