## Local interpolation by
a quadratic Lagrange finite element in 1D

*Josef Dalik*

**Address****.**

Brno University of
Technology, Faculty of
Civil Engineering, Department of
Mathematics, Zizkova 17,
662 37 Brno, Czech Republic

**E-mail**. dalik.j@fce.vutbr.cz

**Abstract****.**

We analyse the error of interpolation
of functions from the space
$H^3(a,c)$ in the nodes
$a<b<c$ of a

regular quadratic
Lagrange finite element in
1D by interpolants from the local function
space of this finite element. We show that

the order
of the error
depends on the way in which the
mutual positions of nodes $a,b,c$ change as the length
of interval $[a,c]$ approaches
zero.

**AMSclassification**.
65D05, 65L60.

**Keywords****. **Quadratic Lagrange finite elements in 1D, local interpolation of functions in one variable.