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

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.