Publication result 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

English Title

Operators approximating partial derivatives at vertices of triangulations by averaging

Type

Peer-reviewed article not indexed in WoS or Scopus

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.

English 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

Key words in English

partial derivative; high-order approximation; recovery operator

Authors

DALÍK, J.

RIV year

2011

Released

29.11.2010

Publisher

Matematický ústav AV ČR

Location

Praha

ISBN

0862-7959

Periodical

Mathematica Bohemica

Volume

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"
}