Publication detail

Operators approximating partial derivatives at vertices of triangulations by averaging

DALÍK, J.

Original Title

Operators approximating partial derivatives at vertices of triangulations by averaging

Type

journal article - other

Language

English

Original Abstract

We study the problem of a high-order approximation of the partial derivatives of smooth functions u in the vertices of triangulations under the assumption that the values of u are known in the vertices of the given triangulation only. An operator A computing these approximations is said to be consistent when, for every vertex a, the approximations A(u) (a) are equal to the partial derivative of u at a for all polynomials u of degree less than or equal to two. We characterize all consistent averaging operators and show that, in general, there exists no consistent approximation of the gradient of a smooth function u by averaging.

Keywords

partial derivative; high-order approximation; recovery operator

Authors

DALÍK, J.

RIV year

2010

Released

29. 11. 2010

Publisher

Matematický ústav AV ČR

Location

Praha

ISBN

0862-7959

Periodical

Mathematica Bohemica

Year of study

2010 (135)

Number

4

State

Czech Republic

Pages from

363

Pages to

372

Pages count

10

BibTex

@article{BUT49958,
  author="Josef {Dalík}",
  title="Operators approximating partial derivatives at vertices of triangulations by averaging",
  journal="Mathematica Bohemica",
  year="2010",
  volume="2010 (135)",
  number="4",
  pages="363--372",
  issn="0862-7959"
}