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KIAM Preprint  17, Moscow, 2023
Authors: Khaytaliev I.R., Shilnikov E.V.
Solution of convection-diffusion equations by local discontinuous Galerkin method
Abstract:
In the work, the discontinuous Galerkin method (LDG) is applied to solving linear and nonlinear convection-diffusion problems. The idea of this method is to transform high-order equations into a system of first-order equations, and then apply the classical discontinuous Galerkin method (DG) to this system. An orthogonal system of Legendre polynomials is chosen as the system of basis functions. The cases of both continuous and discontinuous solutions of the problem are considered. The dependence of the accuracy and stability of the method on the step of the spatial grid and the number of basis functions is investigated. The application of parallel computing to the algorithm is investigated. In the future, it is proposed to apply the LRG method for solving the problems of modeling gas mixtures flows.
Keywords:
local discontinuous Galerkin method, Legendre polynomials, Burgers equation, solution accuracy, algorithm stability, parallel calculations
Publication language: russian,  pages: 27
Research direction:
Mathematical problems and theory of numerical methods
Russian source text:
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About authors:
  • Khaytaliev Ismatolo Ramazanovich,  orcid.org/0000-0002-6552-613XMoscow Automobile and Road Construction State Technical University (MADI)
  • Shilnikov Evgeny Vladimirovich,  orcid.org/0000-0002-4932-9849KIAM RAS