Geodesic
Optimal-order quadratic interpolation in vertices of unstructured triangulations
Applications of Mathematics, Tome 53 (2008) no. 6, pp. 547-560

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

We study the problem of Lagrange interpolation of functions of two variables by quadratic polynomials under the condition that nodes of interpolation are vertices of a triangulation. For an extensive class of triangulations we prove that every inner vertex belongs to a local six-tuple of vertices which, used as nodes of interpolation, have the following property: For every smooth function there exists a unique quadratic Lagrange interpolation polynomial and the related local interpolation error is of optimal order. The existence of such six-tuples of vertices is a precondition for a successful application of certain post-processing procedures to the finite-element approximations of the solutions of differential problems.
DOI : 10.1007/s10492-008-0041-x
Classification : 41A05, 41A10, 41A63, 65D05
Keywords: interpolation of functions of two variables; strongly regular classes of triangulations; poised sets of vertices 
@article{10_1007_s10492_008_0041_x,
     author = {Dal{\'\i}k, Josef},
     title = {Optimal-order quadratic interpolation in vertices of unstructured triangulations},
     journal = {Applications of Mathematics},
     pages = {547--560},
     publisher = {mathdoc},
     volume = {53},
     number = {6},
     year = {2008},
     doi = {10.1007/s10492-008-0041-x},
     mrnumber = {2469065},
     zbl = {1199.41006},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1007/s10492-008-0041-x/}
}
TY  - JOUR
AU  - Dalík, Josef
TI  - Optimal-order quadratic interpolation in vertices of unstructured triangulations
JO  - Applications of Mathematics
PY  - 2008
SP  - 547
EP  - 560
VL  - 53
IS  - 6
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.1007/s10492-008-0041-x/
DO  - 10.1007/s10492-008-0041-x
LA  - en
ID  - 10_1007_s10492_008_0041_x
ER  - 
%0 Journal Article
%A Dalík, Josef
%T Optimal-order quadratic interpolation in vertices of unstructured triangulations
%J Applications of Mathematics
%D 2008
%P 547-560
%V 53
%N 6
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.1007/s10492-008-0041-x/
%R 10.1007/s10492-008-0041-x
%G en
%F 10_1007_s10492_008_0041_x
Dalík, Josef. Optimal-order quadratic interpolation in vertices of unstructured triangulations. Applications of Mathematics, Tome 53 (2008) no. 6, pp. 547-560. doi: 10.1007/s10492-008-0041-x

Cité par Sources :