Article
Full entry |
PDF
(0.2 MB)
Feedback
PDF
(0.2 MB)
Feedback
Keywords:
quadratic Lagrange finite elements in 1D; local interpolation of functions in one variable
quadratic Lagrange finite elements in 1D; local interpolation of functions in one variable
Summary:
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.
References:
[1] Hutson V. C. L., Pym J. S. : Applications of Functional Analysis and Operator Theory. Academic Press, London, 1980. MR 0569354 | Zbl 0426.46009
[2] Křížek M., Neittaanmäki P.: Finite Element Approximation of Variational Problems and Applications. Longman Scientific & Technical, Essex, 1990. MR 1066462 | Zbl 0708.65106
[3] Nečas J.: Les méthodes directes en théorie des équations elliptiques. Masson et C${}^{ie}$, Éditeurs, Paris; Academia, Éditeurs, Prague, 1967. MR 0227584
[4] Rudin W.: Principles of Mathematical Analysis. McGraw-Hill, New York, 1964. MR 0166310 | Zbl 0148.02903
[5] Strang G., Fix G. J.: An Analysis of the Finite Element Method. Prentice Hall, Englewood Clifs, N. J., 1973. MR 0443377 | Zbl 0356.65096
[6] Ženíšek A.: Nonlinear Elliptic and Evolution Problems and Their Finite Element Approximations. Academic Press, London, 1990. MR 1086876
Search
Partner of
