Mathematics and Statistics Faculty Publications

Title

A General Mixed Covolume Framework for Constructing Conservative Schemes for Elliptic Problems

Document Type

Article

Abstract

We present a general framework for the finite volume or covolume schemes developed for second order elliptic problems in mixed form, i.e., written as first order systems. We connect these schemes to standard mixed finite element methods via a one-to-one transfer operator between trial and test spaces. In the nonsymmetric case (convection-diffusion equation) we show one-half order convergence rate for the flux variable which is approximated either by the lowest order Raviart-Thomas space or by its image in the space of discontinuous piecewise constants. In the symmetric case (diffusion equation) a first order convergence rate is obtained for both the state variable (e.g., concentration) and its flux. Numerical experiments are included.

Publication Date

1999

Publication Title

Mathematics of Computation of the American Mathematical Society

Volume

68

Issue

227

Start Page No.

991

End Page No.

1011

ISSN

0025-5718

DOI

10.1090/S0025-5718-99-01090-X