## 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.

#### Copyright Statement

Publisher PDF

#### Repository Citation

Chou, So-Hsiang and Vassilevski, Panayot, "A General Mixed Covolume Framework for Constructing Conservative Schemes for Elliptic Problems" (1999). *Mathematics and Statistics Faculty Publications*. 46.

https://scholarworks.bgsu.edu/math_stat_pub/46

#### Publication Date

1999

#### Publication Title

Mathematics of Computation of the American Mathematical Society