| Title:
|
The invertibility of the isoparametric mappings for triangular quadratic Lagrange finite elements (English) |
| Author:
|
Dalík, Josef |
| Language:
|
English |
| Journal:
|
Applications of Mathematics |
| ISSN:
|
0862-7940 (print) |
| ISSN:
|
1572-9109 (online) |
| Volume:
|
57 |
| Issue:
|
5 |
| Year:
|
2012 |
| Pages:
|
445-462 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
A reference triangular quadratic Lagrange finite element consists of a right triangle $\hat K$ with unit legs $S_1$, $S_2$, a local space $\hat {\mathcal L}$ of quadratic polynomials on $\hat K$ and of parameters relating the values in the vertices and midpoints of sides of $\hat K$ to every function from $\hat {\mathcal L}$. Any isoparametric triangular quadratic Lagrange finite element is determined by an invertible isoparametric mapping ${\mathcal F}_h=(F_1,F_2)\in \hat {\mathcal L}\times \hat {\mathcal L}$. We explicitly describe such invertible isoparametric mappings ${\mathcal F}_h$ for which the images ${\mathcal F}_h(S_1)$, ${\mathcal F}_h(S_2)$ of the segments $S_1$, $S_2$ are segments, too. In this way we extend the well-known result going back to W. B. Jordan, 1970, characterizing those invertible isoparametric mappings whose restrictions to the segments $S_1$ and $S_2$ are linear. (English) |
| Keyword:
|
isoparametric triangular quadratic Lagrange finite element |
| Keyword:
|
invertible isoparametric mapping |
| Keyword:
|
initial or boundary value problems |
| MSC:
|
65M50 |
| MSC:
|
65M60 |
| MSC:
|
65N30 |
| MSC:
|
65N50 |
| idZBL:
|
Zbl 1265.65233 |
| idMR:
|
MR2984613 |
| DOI:
|
10.1007/s10492-012-0026-7 |
| . |
| Date available:
|
2012-08-19T21:56:05Z |
| Last updated:
|
2020-07-02 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/142910 |
| . |
| Reference:
|
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| Reference:
|
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| Reference:
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| Reference:
|
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| Reference:
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| . |
