Mixed covolume methods for elliptic problems on triangular grids

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We consider a covolume or finite volume method for a system of first-order PDEs resulting from the mixed formulation of the variable coefficient-matrix Poisson equation with the Neumann boundary condition. The system may represent either the Darcy law and the mass conservation law in anisotropic porous media flow, or Fourier law and energy conservation. The velocity and pressure are approximated by the lowest order Raviart-Thomas space on triangles. We prove its first-order optimal rate of convergence for the approximate velocities in the L-2 -and H(div; Omega)-norms as well as for the approximate pressures in the L-2-norm. Numerical experiments are included.
Publisher
SIAM PUBLICATIONS
Issue Date
1998-10
Language
English
Article Type
Article
Keywords

CONVERGENCE

Citation

SIAM JOURNAL ON NUMERICAL ANALYSIS, v.35, no.5, pp.1850 - 1861

ISSN
0036-1429
URI
http://hdl.handle.net/10203/72100
Appears in Collection
MA-Journal Papers(저널논문)
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