Finite element based hybrid techniques for advection-diffusion-reaction processes

• Published in: An international journal of optimization and control Vol. 8; no. 2; pp. 127 - 136
• Main Authors: Sari, Murat, Tunc, Huseyin
• Format: Journal Article
• Language: English
• Published: Balikesir Balikesir University, Faculty of Engineering Department of Industrial Engineering 2018; Balikesir University
• Subjects: Advection; advection-diffusion-reaction process; B-spline; Basis functions; Collocation methods; Diffusion; Finite element method; Galerkin method; Reaction-diffusion equations; Taylor-Galerkin method
• ISSN: 2146-0957; 2146-5703
• DOI: 10.11121/ijocta.01.2018.00452

In this paper, numerical solutions of the advection-diffusion-reaction (ADR) equation are investigated using the Galerkin, collocation and Taylor-Galerkin cubic B-spline finite element method in strong form of spatial elements using an ?-family optimization approach for time variation. The main objective of this article is to capture effective results of the finite element techniques with B-spline basis functions under the consideration of the ADR processes. All produced results are compared with the exact solution and the literature for various versions of problems including pure advection, pure diffusion, advection-diffusion, and advection-diffusion-reaction equations. It is proved that the present methods have good agreement with the exact solution and the literature.