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Discontinuous finite-element Galerkin method for numerical solution of two-dimensional diffusion problems on unstructured grids

V. F. Masyagin1, R. V. Zhalnin2, V. F. Tishkin3

AnnotationThe new effective solution algorithm for parabolic equations on base of discontinuous Galerkin method is offered, which has convergence and accuracy when using the explicit scheme. Distinctive feature of the offered method is the use of the dual grid for finding a part of the parameters. The research method is exemplified by the initial-boundary problem for two-dimensional heat conduction equation. Сalculations of two-dimensional modeling problems have shown a good accuracy of offered method.
Keywordsparabolic equations, discontinuous Galerkin methods, сonvergence and accuracy of the method.

1Postgraduate student of Applied Mathematics Chair, Mordovian State University after N.P. Ogarev, Saransk; vmasyagin@gmail.com.

2Assistant Professor of Applied Mathematics Chair, Mordovian State University after N.P. Ogarev, Saransk; zhalnin@gmail.com.

3Deputy Director of the Institute of applied mathematics by name M.V. Keldysh of RAS, Moscow; tishkin@imamod.ru.

Citation: V. F. Masyagin, R. V. Zhalnin, V. F. Tishkin, "[Discontinuous finite-element Galerkin method for numerical solution of two-dimensional diffusion problems on unstructured grids]", Zhurnal Srednevolzhskogo matematicheskogo obshchestva,15:2 (2013) 59–65 (In Russian)