NEW QUADRILATERAL MIXED FINITE ELEMENTS

Cited 1 time in webofscience Cited 0 time in scopus
  • Hit : 433
  • Download : 162
In this paper, we introduce a new family of mixed finite element spaces of higher order (k >= 1) on general quadrilateral grids. A typical element has two fewer degrees of freedom than the well-known Raviart-Thomas finite element RT([k]), yet enjoys an optimal-order approximation for the velocity in L(2)-norm. The order of approximation in the divergence norm is one less than the velocity, as is common to all other known elements, except for a recent element introduced by Arnold et al. [SIAM J. Numer. Anal., 42 (2005), pp. 2429-2451]. However, we introduce a local post-processing technique to obtain an optimal order in L(2)-norm of divergence. This technique can be used to enhance the result of RT([k]) element as well, and hence, can be easily incorporated into existing codes. Our element has one lower order of approximation in pressure than the RT([k]) element. However, the pressure also can be locally post-processed to produce an optimal-order approximation. The greatest advantage of our finite element lies in the fact that it has the fewest degrees of freedom among all the known quadrilateral mixed finite elements and thus, together with the post-processing techniques, provides a very efficient way of computing flow variables in mixed formulation. Numerical examples are in quite good agreement with the theory even for the case of almost degenerate quadrilateral grids.
Publisher
KENT STATE UNIVERSITY
Issue Date
2010
Language
English
Article Type
Article
Keywords

ELLIPTIC PROBLEMS; VOLUME METHODS; GRIDS

Citation

ELECTRONIC TRANSACTIONS ON NUMERICAL ANALYSIS, v.37, pp.189 - 201

ISSN
1068-9613
URI
http://hdl.handle.net/10203/98743
Appears in Collection
MA-Journal Papers(저널논문)
Files in This Item
000285976700012.pdf(155.41 kB)Download
This item is cited by other documents in WoS
⊙ Detail Information in WoSⓡ Click to see webofscience_button
⊙ Cited 1 items in WoS Click to see citing articles in records_button

qr_code

  • mendeley

    citeulike


rss_1.0 rss_2.0 atom_1.0