A Combination of a Special Hermite Finite Element with Collocation for a Reaction-Diffusion Type Equation


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Abstract

In the paper, we propose an efficient method based on the use of a bicubic Hermite finite element coupled with collocation for the reaction-diffusion equation with a variable coefficient. This enables one to reduce the dimension of the system of equations in comparison with the standard finite element scheme. Numerical experiments confirm a theoretical convergence estimate and demonstrate the advantage of the proposed method.

About the authors

L. V. Gileva

Institute of Computational Modelling, Siberian Branch; Siberian Federal University

Author for correspondence.
Email: gileva@icm.krasn.ru
Russian Federation, Krasnoyarsk, 660036; Krasnoyarsk, 660041

E. D. Karepova

Institute of Computational Modelling, Siberian Branch; Siberian Federal University

Author for correspondence.
Email: e.d.karepova@icm.krasn.ru
Russian Federation, Krasnoyarsk, 660036; Krasnoyarsk, 660041

V. V. Shaidurov

Institute of Computational Modelling, Siberian Branch; Siberian Federal University

Author for correspondence.
Email: shaidurov04@mail.ru
Russian Federation, Krasnoyarsk, 660036; Krasnoyarsk, 660041

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