Interpolation of non-smooth functions on anisotropic finite element meshes

Thomas Apel

ESAIM: Mathematical Modelling and Numerical Analysis (2010)

  • Volume: 33, Issue: 6, page 1149-1185
  • ISSN: 0764-583X

Abstract

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In this paper, several modifications of the quasi-interpolation operator of Scott and Zhang [30] are discussed. The modified operators are defined for non-smooth functions and are suited for application on anisotropic meshes. The anisotropy of the elements is reflected in the local stability and approximation error estimates. As an application, an example is considered where anisotropic finite element meshes are appropriate, namely the Poisson problem in domains with edges.

How to cite

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Apel, Thomas. "Interpolation of non-smooth functions on anisotropic finite element meshes." ESAIM: Mathematical Modelling and Numerical Analysis 33.6 (2010): 1149-1185. <http://eudml.org/doc/197422>.

@article{Apel2010,
abstract = { In this paper, several modifications of the quasi-interpolation operator of Scott and Zhang [30] are discussed. The modified operators are defined for non-smooth functions and are suited for application on anisotropic meshes. The anisotropy of the elements is reflected in the local stability and approximation error estimates. As an application, an example is considered where anisotropic finite element meshes are appropriate, namely the Poisson problem in domains with edges. },
author = {Apel, Thomas},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis},
keywords = { Anisotropic finite elements; interpolation error estimate; quasi-interpolation; non-smooth functions; edge singularity; reaction diffusion problem.; quasi-interpolation operator; anisotropic meshes; finite element; local stability; error estimates; Poisson problem},
language = {eng},
month = {3},
number = {6},
pages = {1149-1185},
publisher = {EDP Sciences},
title = {Interpolation of non-smooth functions on anisotropic finite element meshes},
url = {http://eudml.org/doc/197422},
volume = {33},
year = {2010},
}

TY - JOUR
AU - Apel, Thomas
TI - Interpolation of non-smooth functions on anisotropic finite element meshes
JO - ESAIM: Mathematical Modelling and Numerical Analysis
DA - 2010/3//
PB - EDP Sciences
VL - 33
IS - 6
SP - 1149
EP - 1185
AB - In this paper, several modifications of the quasi-interpolation operator of Scott and Zhang [30] are discussed. The modified operators are defined for non-smooth functions and are suited for application on anisotropic meshes. The anisotropy of the elements is reflected in the local stability and approximation error estimates. As an application, an example is considered where anisotropic finite element meshes are appropriate, namely the Poisson problem in domains with edges.
LA - eng
KW - Anisotropic finite elements; interpolation error estimate; quasi-interpolation; non-smooth functions; edge singularity; reaction diffusion problem.; quasi-interpolation operator; anisotropic meshes; finite element; local stability; error estimates; Poisson problem
UR - http://eudml.org/doc/197422
ER -

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