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.
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Gileva, L.V., Karepova, E.D. & Shaidurov, V.V. A Combination of a Special Hermite Finite Element with Collocation for a Reaction-Diffusion Type Equation. Lobachevskii J Math 40, 459–468 (2019). https://doi.org/10.1134/S1995080219040085
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DOI: https://doi.org/10.1134/S1995080219040085