# Interpolation of non-smooth functions on anisotropic finite element meshes

ESAIM: Mathematical Modelling and Numerical Analysis (2010)

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

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topApel, 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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