A method of increasing the order of the weak approximation of the laws of conservation on discontinuous solutions.

*(English. Russian original)*Zbl 0911.65079
Comput. Math. Math. Phys. 36, No. 10, 1443-1451 (1996); translation from Zh. Vychisl. Mat. Mat. Fiz. 36, No. 10, 146-157 (1996).

Summary: Using the example of explicit conservative difference schemes on two time layers, the possibility of using differential and integral implications of the laws of conservation to increase the order of weak approximation of the laws of conservation on discontinuous solutions is analyzed. Each differential implication of a linear differential equation has an integral analogue, by virtue of which in linear difference schemes the orders of approximation on smooth and discontinuous solutions are the same. There are no such integral analogues in the general case for quasilinear conservation laws, and thus increasing the order of the local approximation on smooth solutions in nonlinear schemes does not necessarily yield a similar increase in the order of weak approximation on generalized solutions.

##### MSC:

65M15 | Error bounds for initial value and initial-boundary value problems involving PDEs |

65M06 | Finite difference methods for initial value and initial-boundary value problems involving PDEs |

35L65 | Hyperbolic conservation laws |