The problem of keeping the high order of the solution and providing it’s monotony is of current importance. To solve this problem the usage of smoothing operator is proposed instead of limiting. Theoretically it doesn’t demote the order of method.

Discontinuous Galerkin methods, WENO reconstruction, smoothing operator

Mathematical modelling in actual problems of science and technics

Ladonkina Marina Eugenievna,  ,  orcid.org/0000-0001-7596-1672,  KIAM RAS

Neklyudova Olga Alexandrovna,  ,  orcid.org/0000-0001-9465-4782,  KIAM RAS

Tishkin Vladimir Fedorovich,  ,  orcid.org/0000-0001-7295-7002,  KIAM RAS