Mixed finite volume methods on nonstaggered quadrilateral grids for elliptic problems

Authors:
So-Hsiang Chou, Do Y. Kwak and Kwang Y. Kim

Journal:
Math. Comp. **72** (2003), 525-539

MSC (2000):
Primary 65F15, 65N30, 35J60

DOI:
https://doi.org/10.1090/S0025-5718-02-01426-6

Published electronically:
March 21, 2002

MathSciNet review:
1954955

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Abstract: We construct and analyze a mixed finite volume method on quadrilateral grids for elliptic problems written as a system of two first order PDEs in the state variable (e.g., pressure) and its flux (e.g., Darcy velocity). An important point is that no staggered grids or covolumes are used to stabilize the system. Only a single primary grid system is adopted, and the degrees of freedom are imposed on the interfaces. The approximate flux is sought in the lowest-order Raviart-Thomas space and the pressure field in the rotated- nonconforming space. Furthermore, we demonstrate that the present finite volume method can be interpreted as a rotated- nonconforming finite element method for the pressure with a simple local recovery of flux. Numerical results are presented for a variety of problems which confirm the usefulness and effectiveness of the method.

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Additional Information

**So-Hsiang Chou**

Affiliation:
Department of Mathematics and Statistics, Bowling Green State University, Bowling Green, Ohio 43403

Email:
chou@bgnet.bgsu.edu

**Do Y. Kwak**

Affiliation:
Department of Mathematics, Korea Advanced Institute of Science and Technology, Taejon, Korea 305-701

Email:
dykwak@math.kaist.ac.kr

**Kwang Y. Kim**

Affiliation:
Department of Mathematics, Korea Advanced Institute of Science and Technology, Taejon, Korea 305-701

Email:
kky@mathx.kaist.ac.kr

DOI:
https://doi.org/10.1090/S0025-5718-02-01426-6

Keywords:
Mixed method,
finite volume method,
box method,
quadrilateral grid

Received by editor(s):
November 14, 2000

Received by editor(s) in revised form:
May 29, 2001

Published electronically:
March 21, 2002

Additional Notes:
The research of the first author was supported by NSF grant DMS-0074259

The research of the second and third authors was supported by BK21 project, Korea and by grant No. 2000-2-10300-001-5 from the Basic Research Program of the Korea Science & Engineering Foundation

Article copyright:
© Copyright 2002
American Mathematical Society