| Title:
|
Optimal-order quadratic interpolation in vertices of unstructured triangulations (English) |
| Author:
|
Dalík, Josef |
| Language:
|
English |
| Journal:
|
Applications of Mathematics |
| ISSN:
|
0862-7940 (print) |
| ISSN:
|
1572-9109 (online) |
| Volume:
|
53 |
| Issue:
|
6 |
| Year:
|
2008 |
| Pages:
|
547-560 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
interpolation of functions of two variables |
| Keyword:
|
strongly regular classes of triangulations |
| Keyword:
|
poised sets of vertices |
| MSC:
|
41A05 |
| MSC:
|
41A10 |
| MSC:
|
41A63 |
| MSC:
|
65D05 |
| idZBL:
|
Zbl 1199.41006 |
| idMR:
|
MR2469065 |
| DOI:
|
10.1007/s10492-008-0041-x |
| . |
| Date available:
|
2010-07-20T12:39:07Z |
| Last updated:
|
2020-07-02 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/140340 |
| . |
| Reference:
|
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