DISCONTINUOUS GALERKIN METHOD FOR NUMERICAL SOLUTION OF TWO-DIMENSIONAL DIFFUSION PROBLEMS ON UNSTRUCTURAL STAGERRED GRIDS

Zhalnin R.V, Masyagin V.F, Panyushkina E.N

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The new effective solution algorithm for diffusion-type problems on base of discontinuous Galerkin method is offered, which has convergence and accuracy when using the explicit scheme. In contrast to the classical discontinuous Galerkin method, this algorithm does not require an additional way of finding fluxes at the elements of the main grid due to the fact that the gradients are sought on the dual grid, and the desired function – on the main grid. As the dual grid cells are used barycentric volumes constructed relative to the nodes of the main grid. The research method is exemplified by the initial-boundary problem for two-dimensional heat conduction equation. Calculations of two-dimensional modeling problems have shown a good accuracy of offered method. Efficiency of the method on the «bad» grids is shown.

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Жалнин Р.В, Масягин В.Ф, Панюшкина Е.Н О ПРИМЕНЕНИИ РАЗРЫВНОГО МЕТОДА ГАЛЕРКИНА ДЛЯ ЧИСЛЕННОГО РЕШЕНИЯ ДВУМЕРНЫХ УРАВНЕНИЙ ДИФФУЗИОННОГО ТИПА НА НЕСТРУКТУРИРОВАННЫХ РАЗНЕСЕННЫХ СЕТКАХ // Научное обозрение. Физико-математические науки . 2020. № 1. С. 30-30;
URL: https://physics-mathematics.ru/en/article/view?id=30 (дата обращения: 24.06.2026).