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

Autor:	Josef Dalík
Rok vydání:	2012
Předmět:	Applied Mathematics Mathematical analysis Function (mathematics) Midpoint Finite element method law.invention Combinatorics Quadratic equation Invertible matrix Local space law Mathematics::Differential Geometry Unit (ring theory) Right triangle Mathematics
Zdroj:	Applications of Mathematics. 57:445-462
ISSN:	1572-9109 0862-7940
DOI:	10.1007/s10492-012-0026-7
Popis:	A reference triangular quadratic Lagrange finite element consists of a right triangle \(\hat K\) with unit legs S1, S2, a local space \(\hat L\) 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 \(\hat L\). Any isoparametric triangular quadratic Lagrange finite element is determined by an invertible isoparametric mapping \({F_h} = ({F_1},{F_2}) \in \hat L \times \hat L\). We explicitly describe such invertible isoparametric mappings Fh for which the images Fh(S1), Fh(S2) of the segments S1, S2 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 S1 and S2 are linear.
Databáze:	OpenAIRE
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