Discontinuous finite-element Galerkin method for numerical solution of two-dimensional diffusion problems on unstructured grids
R. V. Zhalnin1, M. Ye. Ladonkina2, V. F. Masyagin3, V. F. Tishkin4
| Annotation | The new effective solution algorithm for diffusion type equations on base of discontinuous Galerkin method is offered, which has good convergence and accuracy when using the explicit scheme. A characteristic feature of the offered method is to use a dual mesh on which the solution is sought of ancillary parameters. Investigation of the method is exemplified by the initial-boundary value problem for two-dimensional heat equation. Сalculations of two-dimensional modeling problems including with explosive factors have shown a good accuracy of offered method. |
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| Keywords | parabolic equations, discontinuous Galerkin method, сonvergence and accuracy of the method. |
1Head of Department of Applied Mathematics, Differential Equations and Theoretical Mechanics Chair, Mordovian State University after N.P. Ogarev, Saransk; zhalnin@gmail.com.
2Senior Researcher of the Institute of applied mathematics by name M.V. Keldysh of RAS, Moscow; ladonkina@imamod.ru.
3Postgraduate student of Applied Mathematics, Differential Equations and Theoretical Mechanics Chair, Mordovian State University after N.P. Ogarev, Saransk; vmasyagin@gmail.com.
4Deputy Director for Science of the Institute of applied mathematics by name M.V. Keldysh of RAS, Moscow; v.f.tishkin@mail.ru.
Citation: R. V. Zhalnin, M. Ye. Ladonkina, V. F. Masyagin, V. F. Tishkin, "[Discontinuous finite-element Galerkin method for numerical solution of two-dimensional diffusion problems on unstructured grids]", Zhurnal Srednevolzhskogo matematicheskogo obshchestva,16:2 (2014) 7–13 (In Russian)
