Convergence of a finite volume - mixed finite element method for an elliptic - hyperbolic system
نویسندگان
چکیده
This paper gives a proof of convergence for the approximate solution of an elliptic-hyperbolic system, describing the conservation of two immiscible incompressible phases flowing in a porous medium. The approximate solution is obtained by a mixed finite element method on a large class of meshes for the elliptic equation and a finite volume method for the hyperbolic equation. Since the considered meshes are not necessarily structured, the proof uses a weak total variation inequality, which cannot yield a BV-estimate. We thus prove, under an L∞ estimate, the weak convergence of the finite volume approximation. The strong convergence proof is then sketched under regularity assumptions which ensure that the flux is Lipschitz-continuous.
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Convergence of a finite volume scheme for an elliptic-hyperbolic system
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