Application of the discontinuous Galerkin method for numerical solution of the quasi-linear advection equation

The paper is dedicated to the testing of discontinuous Galerkin method for numerical solution of quasi - linear advection equation, as well as its comparison with other well-known schemes. The comparison was carried out between different variants of the discontinuous Galerkin method and schemes considered in [2]. The presented information about the errors of numerical solutions allows to compare the quality of the schemes. Analysis of the errors has shown that the studied method gives higher accuracy in the broad range of Courant numbers, as well as smaller ‘spreading’ of shock solutions.