| Title:
|
On stability of the $P^{\rm mod}_ n/P_ n$ element for incompressible flow problems (English) |
| Author:
|
Knobloch, Petr |
| Language:
|
English |
| Journal:
|
Applications of Mathematics |
| ISSN:
|
0862-7940 (print) |
| ISSN:
|
1572-9109 (online) |
| Volume:
|
51 |
| Issue:
|
5 |
| Year:
|
2006 |
| Pages:
|
473-493 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
It is well known that finite element spaces used for approximating the velocity and the pressure in an incompressible flow problem have to be stable in the sense of the inf-sup condition of Babuška and Brezzi if a stabilization of the incompressibility constraint is not applied. In this paper we consider a recently introduced class of triangular nonconforming finite elements of $n$th order accuracy in the energy norm called $P_n^{}$ elements. For $n\le 3$ we show that the stability condition holds if the velocity space is constructed using the $P_n^{}$ elements and the pressure space consists of continuous piecewise polynomial functions of degree $n$. (English) |
| Keyword:
|
nonconforming finite element method |
| Keyword:
|
inf-sup condition |
| Keyword:
|
incompressible flow problem |
| MSC:
|
65N12 |
| MSC:
|
65N30 |
| MSC:
|
76D05 |
| MSC:
|
76M10 |
| idZBL:
|
Zbl 1164.76325 |
| idMR:
|
MR2261635 |
| DOI:
|
10.1007/s10492-006-0017-7 |
| . |
| Date available:
|
2009-09-22T18:26:58Z |
| Last updated:
|
2020-07-02 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/134649 |
| . |
| Reference:
|
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