The invertibility of the isoparametric mappings for triangular quadratic Lagrange finite elements

Dalík, Josef. "The invertibility of the isoparametric mappings for triangular quadratic Lagrange finite elements." Applications of Mathematics 57.5 (2012): 445-462. <http://eudml.org/doc/247048>.

@article{Dalík2012,
abstract = {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.},
author = {Dalík, Josef},
journal = {Applications of Mathematics},
keywords = {isoparametric triangular quadratic Lagrange finite element; invertible isoparametric mapping; initial or boundary value problems; isoparametric triangular quadratic Lagrange finite element; invertible isoparametric mapping; initial or boundary value problems},
language = {eng},
number = {5},
pages = {445-462},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {The invertibility of the isoparametric mappings for triangular quadratic Lagrange finite elements},
url = {http://eudml.org/doc/247048},
volume = {57},
year = {2012},
}

TY - JOUR
AU - Dalík, Josef
TI - The invertibility of the isoparametric mappings for triangular quadratic Lagrange finite elements
JO - Applications of Mathematics
PY - 2012
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 57
IS - 5
SP - 445
EP - 462
AB - 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.
LA - eng
KW - isoparametric triangular quadratic Lagrange finite element; invertible isoparametric mapping; initial or boundary value problems; isoparametric triangular quadratic Lagrange finite element; invertible isoparametric mapping; initial or boundary value problems
UR - http://eudml.org/doc/247048
ER -