Convergence of an upstream finite volume scheme for a nonlinear hyperbolic equation on a triangular mesh.
On some implicit and semi-implicit staggered schemes for the shallow water and Euler equations
In this paper, we propose implicit and semi-implicit in time finite volume schemes for the barotropic Euler equations (hence, as a particular case, for the shallow water equations) and for the full Euler equations, based on staggered discretizations. For structured meshes, we use the MAC finite volume scheme, and, for general mixed quadrangular/hexahedral and simplicial meshes, we use the discrete unknowns of the Rannacher−Turek or Crouzeix−Raviart finite elements. We first show that a solution...
Finite volume schemes for nonlinear parabolic problems: another regularization method
Analysis tools for finite volume schemes
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