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

In this paper, numerical solutions of the advection-diffusion-reaction (ADR)equation are investigated using the Galerkin, collocation and Taylor-Galerkincubic B-spline finite element methods in strong form of spatial elements using anα-family optimization approach for time variation. The main objective of thisarticle is to capture effective results of the finite element techniques with Bsplinebasis functions under the consideration of the ADR processes. Allproduced results are compared with the exact solution and the literature forvarious versions of problems including pure advection, pure diffusion, advectiondiffusion,and advection-diffusion-reaction equations. It is proved that thepresent methods have good agreement with the exact solution and the literature.

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