Detail publikačního výsledku

Operators approximating partial derivatives at vertices of triangulations by averaging

DALÍK, J.

Originální název

Operators approximating partial derivatives at vertices of triangulations by averaging

Anglický název

Operators approximating partial derivatives at vertices of triangulations by averaging

Druh

Článek recenzovaný mimo WoS a Scopus

Originální abstrakt

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.

Anglický abstrakt

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.

Klíčová slova

partial derivative; high-order approximation; recovery operator

Klíčová slova v angličtině

partial derivative; high-order approximation; recovery operator

Autoři

DALÍK, J.

Rok RIV

2011

Vydáno

29.11.2010

Nakladatel

Matematický ústav AV ČR

Místo

Praha

ISSN

0862-7959

Periodikum

Mathematica Bohemica

Svazek

2010 (135)

Číslo

4

Stát

Česká republika

Strany od

363

Strany do

372

Strany počet

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"
}