Mortar methods with curved interfaces

B. Flemisch; J. M. Melenk; B. I. Wohlmuth

doi:10.1016/j.apnum.2004.09.007

Mortar methods with curved interfaces

B. Flemisch, J. M. Melenk, B. I. Wohlmuth

Research output: Contribution to journal › Conference article › peer-review

34 Scopus citations

Abstract

We analyze a nonoverlapping domain decomposition technique with curvilinear boundaries. The weak coupling at the curved interfaces is carried out in terms of Lagrange multiplier spaces. We use the abstract framework of mortar and blending elements to obtain a priori results for this nonconforming discretization scheme. Introducing a mesh dependent jump on the curved interfaces based on piecewise linear approximations of the interfaces, the consistency error for the piecewise linear approximation can be decomposed into a consistency error for blending elements and a variational crime. Numerical results illustrate the performance of the method.

Original language	English
Pages (from-to)	339-361
Number of pages	23
Journal	Applied Numerical Mathematics
Volume	54
Issue number	3-4
DOIs	https://doi.org/10.1016/j.apnum.2004.09.007
State	Published - Aug 2005
Externally published	Yes
Event	Selected papers from the 16th Chemnitz Finite Element Symposium 2003 - Duration: 22 Sep 2003 → 24 Sep 2003

Keywords

Curved interface
Curvilinear elements
Domain decomposition
Mortar method

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10.1016/j.apnum.2004.09.007

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title = "Mortar methods with curved interfaces",

abstract = "We analyze a nonoverlapping domain decomposition technique with curvilinear boundaries. The weak coupling at the curved interfaces is carried out in terms of Lagrange multiplier spaces. We use the abstract framework of mortar and blending elements to obtain a priori results for this nonconforming discretization scheme. Introducing a mesh dependent jump on the curved interfaces based on piecewise linear approximations of the interfaces, the consistency error for the piecewise linear approximation can be decomposed into a consistency error for blending elements and a variational crime. Numerical results illustrate the performance of the method.",

keywords = "Curved interface, Curvilinear elements, Domain decomposition, Mortar method",

author = "B. Flemisch and Melenk, {J. M.} and Wohlmuth, {B. I.}",

note = "Funding Information: * Corresponding author. E-mail address: [email protected] (B. Flemisch). 1 Partially supported by Deutsche Forschungsgemeinschaft, SFB 404, C12.; Selected papers from the 16th Chemnitz Finite Element Symposium 2003 ; Conference date: 22-09-2003 Through 24-09-2003",

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doi = "10.1016/j.apnum.2004.09.007",

language = "English",

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AU - Flemisch, B.

AU - Melenk, J. M.

AU - Wohlmuth, B. I.

N1 - Funding Information: * Corresponding author. E-mail address: [email protected] (B. Flemisch). 1 Partially supported by Deutsche Forschungsgemeinschaft, SFB 404, C12.

PY - 2005/8

Y1 - 2005/8

N2 - We analyze a nonoverlapping domain decomposition technique with curvilinear boundaries. The weak coupling at the curved interfaces is carried out in terms of Lagrange multiplier spaces. We use the abstract framework of mortar and blending elements to obtain a priori results for this nonconforming discretization scheme. Introducing a mesh dependent jump on the curved interfaces based on piecewise linear approximations of the interfaces, the consistency error for the piecewise linear approximation can be decomposed into a consistency error for blending elements and a variational crime. Numerical results illustrate the performance of the method.

AB - We analyze a nonoverlapping domain decomposition technique with curvilinear boundaries. The weak coupling at the curved interfaces is carried out in terms of Lagrange multiplier spaces. We use the abstract framework of mortar and blending elements to obtain a priori results for this nonconforming discretization scheme. Introducing a mesh dependent jump on the curved interfaces based on piecewise linear approximations of the interfaces, the consistency error for the piecewise linear approximation can be decomposed into a consistency error for blending elements and a variational crime. Numerical results illustrate the performance of the method.

KW - Curved interface

KW - Curvilinear elements

KW - Domain decomposition

KW - Mortar method

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DO - 10.1016/j.apnum.2004.09.007

M3 - Conference article

AN - SCOPUS:20444471991

SN - 0168-9274

VL - 54

SP - 339

EP - 361

JO - Applied Numerical Mathematics

JF - Applied Numerical Mathematics

IS - 3-4

T2 - Selected papers from the 16th Chemnitz Finite Element Symposium 2003

Y2 - 22 September 2003 through 24 September 2003

ER -

Mortar methods with curved interfaces

Abstract

Keywords

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