Preprint A376/2005
Finite Difference Schemes with Cross Derivatives Correctors for Multidimensional Parabolic Systems

Hermano Frid | Bouchut, François

**Keywords: **
finite difference schemes | quasilinear parabolic systems | cross derivatives | Navier-Stokes equations

We propose finite difference schemes for multidimensional quasilinear parabolic systems whose main feature is the introduction of correctors which control the second-order terms with mixed derivatives. We show that with these correctors the schemes inherit physically relevant properties present at the continuous level, such as the existence of invariant domains and/or the nonincrease of the total amount of entropy. Applications to the compressible Navier-Stokes system are given.