REGULARIZED FINITE ELEMENT METHOD FOR SINGULAR PERTURBED CONVECTION-DIFFUSION-REACTION MODELS WITH NONUNIFORM SOURCES

Roman Drebotiy, Heorhiy Shynkarenko

Анотація


In this paper we present finite element scheme which combines Tikhonov regularization with method of characteristics to reduce Peclet number of original problem to needed value. This will disable oscillations of approximate solution and thus make possible of application standard finite element method with relatively low element count to singular perturbed problems.


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Bartels S. Numerical Approximation of Partial Differential Equations / S. Bartels. – Springer , 2016, – 541 p.


Brenner S. The Mathematical Theory of Finite Element Methods / S. Brenner, L. Scott. – Springer, 2008, 3ed. – 404 p.


Feng X. Recent Developments in Discontinuous Galerkin Finite Element Methods for Partial Differential Equations / X. Feng, O. Karakashian, Y. Xing // The IMA Volumes in Mathematics and its Applications. – 2012, – Volume 157.


Doolan E.P. Uniform numerical methods for problems with initial and boundary layers / E.P. Doolan, J.J.H. Miller, W.H.A. Schilders. – BOOLE PRESS, 1980. – 198 p.


Drebotiy R. On the application of the one hp-adaptive finite element strategy for nonsymmetric convection-diffusion-reaction problems / R. Drebotiy, H. Shynkarenko // Journal of Numerical and Applied Mathematics, ISSN: 0868-6912. – Kyiv, 2017. – Issue 3(126). – P. 48–61.


Logan J. D. Transport modeling in hydrogeochemical systems // New York: Springer, 2001. – 226 p.


Rektorys K. Variational Methods in Mathematics, Science and Engineering. Second edition. – Dr. Reidel Publishing Company, 1980. – 589 p.




DOI: http://dx.doi.org/10.30970/vam.2021.29.11330

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