KIAM Main page Web Library  •  Publication Searh   

KIAM Preprint  17, Moscow, 2023
Authors: Khaytaliev I.R., Shilnikov E.V.
Solution of convection-diffusion equations by local discontinuous Galerkin method
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.
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:
Export link to publication in format:   RIS    BibTeX
View statistics (updated once a day)
over the last 30 days 19 (-4), total hit from 23.03.2023 250
About authors:
  • Khaytaliev Ismatolo Ramazanovich, Automobile and Road Construction State Technical University (MADI)
  • Shilnikov Evgeny Vladimirovich, RAS