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Approximations with piecewise constant fluxes for diffusion equations on polyhedral meshes: algorithms and applications
-
O. Boyarkin
,
Yu.A. Kuznetsov
Published/Copyright:
February 26, 2013
Abstract
In this paper we consider implementation algorithms and applications of the discretization method for diffusion equations on polygonal (2D) and polyhedral (3D) meshes recently proposed by one of the authors in [11]. The discretization method is based on the approximation of fluxes in the mixed finite element method by appropriate piecewise constant vector functions inside the mesh cells. The new piecewise constant fluxes are discontinuous inside the mesh cells but their normal components are continuous on the interfaces between neighbouring cells. Numerical results are given for test problems relevant to applications in reservoir simulation and basin modelling.
Published Online: 2013-02-26
Published in Print: 2012-08
© 2013 by Walter de Gruyter GmbH & Co.
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Articles in the same Issue
- On a posteriori error bounds for approximations of the generalized Stokes problem generated by the Uzawa algorithm
- Approximations with piecewise constant fluxes for diffusion equations on polyhedral meshes: algorithms and applications
- Minimal stencil finite volume scheme with the discrete maximum principle
- Construction of a functional basis with automatic fulfillment of interface conditions at discontinuity points of coefficients of an elliptic operator
- CFD technology for 3D simulation of large-scale hydrodynamic events and disasters
