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We consider the lowest-order Raviart–Thomas mixed finite element
method for second-order elliptic problems on simplicial meshes in
two and three space dimensions. This method produces saddle-point
problems for scalar and flux unknowns. We show how to easily and
locally eliminate the flux unknowns, which implies the equivalence
between this method and a particular multi-point finite volume
scheme, without any approximate numerical integration. The matrix
of the final linear system is sparse, positive...
The subject of the paper is the derivation of error estimates for the combined finite volume-finite element method used for the numerical solution of nonstationary nonlinear convection-diffusion problems. Here we analyze the combination of barycentric finite volumes associated with sides of triangulation with the piecewise linear nonconforming Crouzeix-Raviart finite elements. Under some assumptions on the regularity of the exact solution, the and error estimates are established. At the end...
We propose a bi-dimensional finite volume extension of a continuous ALE method on
unstructured cells whose edges are parameterized by rational quadratic Bezier curves. For
each edge, the control point possess a weight that permits to represent any conic (see for
example [LIGACH]) and thanks to [WAGUSEDE,WAGU], we are able to compute the exact
area of our cells. We then give an extension of scheme for remapping step based
on volume fluxing [MARSHA]...
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