Optimal-order quadratic interpolation in vertices of unstructured triangulations
Applications of Mathematics (2008)
- Volume: 53, Issue: 6, page 547-560
- ISSN: 0862-7940
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topDalík, Josef. "Optimal-order quadratic interpolation in vertices of unstructured triangulations." Applications of Mathematics 53.6 (2008): 547-560. <http://eudml.org/doc/37800>.
@article{Dalík2008,
abstract = {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.},
author = {Dalík, Josef},
journal = {Applications of Mathematics},
keywords = {interpolation of functions of two variables; strongly regular classes of triangulations; poised sets of vertices; interpolation of functions of two variables; strongly regular classes of triangulations; poised sets of vertices},
language = {eng},
number = {6},
pages = {547-560},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Optimal-order quadratic interpolation in vertices of unstructured triangulations},
url = {http://eudml.org/doc/37800},
volume = {53},
year = {2008},
}
TY - JOUR
AU - Dalík, Josef
TI - Optimal-order quadratic interpolation in vertices of unstructured triangulations
JO - Applications of Mathematics
PY - 2008
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 53
IS - 6
SP - 547
EP - 560
AB - 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.
LA - eng
KW - interpolation of functions of two variables; strongly regular classes of triangulations; poised sets of vertices; interpolation of functions of two variables; strongly regular classes of triangulations; poised sets of vertices
UR - http://eudml.org/doc/37800
ER -
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