A general framework for constructing and analyzing mixed finite volume methods on quadrilateral grids: The overlapping covolume case

Cited 35 time in webofscience Cited 0 time in scopus
  • Hit : 206
  • Download : 0
We present a general framework for constructing and analyzing finite volume methods applied to the mixed formulation of second-order elliptic problems on quadrilateral grids. The control volumes, or covolumes, in the grids overlap. An overlapping finite volume method of this type was first introduced by Russell in [T. F. Russell, Tech. report 3, Reservoir Simulation Research Corp., Tulsa, OK, 1995] and was tested for a variety of problems on rectangular and quadrilateral grids in [Z. Cai et al., Comput Geosci., 1 (1997), pp. 289-315]. Later in [S. H. Chou and D. Y. Kwak, SIAM J. Numer. Anal., 37 (2000), pp. 758-771], Chou and Kwak reformulated it as their mixed covolume method and proved optimal order error estimates using the covolume methodology from [S. H. Chou, Math. Comp., 66 (1997), pp. 85-104] and [S. H. Chou and D. Y. Kwak, SIAM J. Numer. Anal., 35 (1998), pp. 494-507]. However, their treatment was restricted to the case of diagonal coefficient tensor and rectangular grids since a different approach was needed for the quadrilateral (distorted rectangular) case. In this paper we give a new framework, which can handle not only the rectangular anisotropic case but also the anisotropic and irregular grid cases in which the locally supported test functions are images of the natural unit coordinate vectors under the Piola transformation. Our theory sheds light on how to create new test functions using quadratures and now covers Russell's quadrilateral case.
Publisher
SIAM PUBLICATIONS
Issue Date
2001-12
Language
English
Article Type
Article
Citation

SIAM JOURNAL ON NUMERICAL ANALYSIS, v.39, no.4, pp.1170 - 1196

ISSN
0036-1429
DOI
10.1137/S003614290037544X
URI
http://hdl.handle.net/10203/83672
Appears in Collection
MA-Journal Papers(저널논문)
Files in This Item
There are no files associated with this item.
This item is cited by other documents in WoS
⊙ Detail Information in WoSⓡ Click to see webofscience_button
⊙ Cited 35 items in WoS Click to see citing articles in records_button

qr_code

  • mendeley

    citeulike


rss_1.0 rss_2.0 atom_1.0