Mathematics and Statistics Faculty Publications

Title

Mixed Covolume Methods for Elliptic Problems on Triangular Grids

Document Type

Article

Abstract

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 L2-and H(div; Q)-norms as well as for the approximate pressures in the L2-norm. Numerical experiments are included.

Publication Date

10-1998

Publication Title

SIAM Journal on Numerical Analysis

Publisher

Society for Industrial and Applied Mathematics

DOI

https://doi.org/10.1137/S0036142997321285

Volume

35

Issue

5

Start Page No.

1850

End Page No.

1861

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