NMA '02 Revised Papers from the 5th International Conference on Numerical Methods and Applications
Mixed finite volume methods on nonstaggered quadrilateral grids for elliptic problems
Mathematics of Computation
Superconvergence of mixed covolume method for elliptic problems on triangular grids
Journal of Computational and Applied Mathematics
A discontinuous mixed covolume method for elliptic problems
Journal of Computational and Applied Mathematics
L2 error estimates and superconvergence of the finite volume element methods on quadrilateral meshes
Advances in Computational Mathematics
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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 $H(\mbox{div};\Omega)$-norms as well as for the approximate pressures in the $L^2$-norm. Numerical experiments are included.