摘要
In this paper, following the paper [7], we analysis the 'sharp' estimate of the rate of entropy dissipation of the fully discrete MUSCL type Godunov schemes by the general compact theory introduced by Coquel-LeFloch [1, 2], and find: because of small viscosity of the above schemes, in the vincity of shock wave, the estimate of the above schemes is more easily obtained, but for rarefaction wave, we must impose a 'sharp' condition on limiter function in order to keep its entropy dissipation and its convergence.
In this paper, following the paper [7], we analysis the 'sharp' estimate of the rate of entropy dissipation of the fully discrete MUSCL type Godunov schemes by the general compact theory introduced by Coquel-LeFloch [1, 2], and find: because of small viscosity of the above schemes, in the vincity of shock wave, the estimate of the above schemes is more easily obtained, but for rarefaction wave, we must impose a 'sharp' condition on limiter function in order to keep its entropy dissipation and its convergence.
