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
DOI
https://doi.org/10.1090/S0025-5718-99-01090-X
Start Page No.
991
End Page No.
1011