| Title:
|
Operators approximating partial derivatives at vertices of triangulations by averaging (English) |
| Author:
|
Dalík, Josef |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
135 |
| Issue:
|
4 |
| Year:
|
2010 |
| Pages:
|
363-372 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Let $\mathcal T_h$ be a triangulation of a bounded polygonal domain $\Omega \subset \Re ^2$, $\mathcal L_h$ the space of the functions from $C(\overline \Omega )$ linear on the triangles from $\mathcal T_h$ and $\Pi _h$ the interpolation operator from $C(\overline \Omega )$ to $\mathcal L_h$. For a unit vector $z$ and an inner vertex $a$ of $\mathcal T_h$, we describe the set of vectors of coefficients such that the related linear combinations of the constant derivatives $\partial \Pi _h(u)/\partial z$ on the triangles surrounding $a$ are equal to $\partial u/\partial z(a)$ for all polynomials $u$ of the total degree less than or equal to two. Then we prove that, generally, the values of the so-called recovery operators approximating the gradient $\nabla u(a)$ cannot be expressed as linear combinations of the constant gradients $\nabla \Pi _h(u)$ on the triangles surrounding $a$. (English) |
| Keyword:
|
partial derivative |
| Keyword:
|
high-order approximation |
| Keyword:
|
recovery operator |
| MSC:
|
65D25 |
| idZBL:
|
Zbl 1224.65057 |
| idMR:
|
MR2681010 |
| DOI:
|
10.21136/MB.2010.140827 |
| . |
| Date available:
|
2010-11-24T08:24:05Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/140827 |
| . |
| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
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| . |
