An Immersed Finite Element Space and Its Approximation Capability

Z. Li; T. Lin; Yanping Lin; R. C. Rogers

doi:10.1002/num.10092

An Immersed Finite Element Space and Its Approximation Capability

Z. Li, T. Lin, Yanping Lin, R. C. Rogers

Research output: Journal article publication › Journal article › Academic research › peer-review

172 Citations (Scopus)

Abstract

This article discusses an immersed finite element (IFE) space introduced for solving a second-order elliptic boundary value problem with discontinuous coefficients (interface problem). The IFE space is nonconforming and its partition can be independent of the interface. The error estimates for the interpolation of a function in the usual Sobolev space indicate that this IFE space has an approximation capability similar to that of the standard conforming linear finite element space based on body-fit partitions. Numerical examples of the related finite element method based on this IFE space are provided.

Original language	English
Pages (from-to)	338-367
Number of pages	30
Journal	Numerical Methods for Partial Differential Equations
Volume	20
Issue number	3
DOIs	https://doi.org/10.1002/num.10092
Publication status	Published - 1 May 2004
Externally published	Yes

Keywords

Error estimates
Finite element
Immersed interface
Interface problems

ASJC Scopus subject areas

Applied Mathematics
Analysis
Computational Mathematics

More information

10.1002/num.10092

Cite this

@article{3ec4a5c23ce14102815a5031bf23072c,

title = "An Immersed Finite Element Space and Its Approximation Capability",

abstract = "This article discusses an immersed finite element (IFE) space introduced for solving a second-order elliptic boundary value problem with discontinuous coefficients (interface problem). The IFE space is nonconforming and its partition can be independent of the interface. The error estimates for the interpolation of a function in the usual Sobolev space indicate that this IFE space has an approximation capability similar to that of the standard conforming linear finite element space based on body-fit partitions. Numerical examples of the related finite element method based on this IFE space are provided.",

keywords = "Error estimates, Finite element, Immersed interface, Interface problems",

author = "Z. Li and T. Lin and Yanping Lin and Rogers, {R. C.}",

year = "2004",

month = may,

day = "1",

doi = "10.1002/num.10092",

language = "English",

volume = "20",

pages = "338--367",

journal = "Numerical Methods for Partial Differential Equations",

issn = "0749-159X",

publisher = "John Wiley and Sons Inc.",

number = "3",

}

TY - JOUR

T1 - An Immersed Finite Element Space and Its Approximation Capability

AU - Li, Z.

AU - Lin, T.

AU - Lin, Yanping

AU - Rogers, R. C.

PY - 2004/5/1

Y1 - 2004/5/1

N2 - This article discusses an immersed finite element (IFE) space introduced for solving a second-order elliptic boundary value problem with discontinuous coefficients (interface problem). The IFE space is nonconforming and its partition can be independent of the interface. The error estimates for the interpolation of a function in the usual Sobolev space indicate that this IFE space has an approximation capability similar to that of the standard conforming linear finite element space based on body-fit partitions. Numerical examples of the related finite element method based on this IFE space are provided.

AB - This article discusses an immersed finite element (IFE) space introduced for solving a second-order elliptic boundary value problem with discontinuous coefficients (interface problem). The IFE space is nonconforming and its partition can be independent of the interface. The error estimates for the interpolation of a function in the usual Sobolev space indicate that this IFE space has an approximation capability similar to that of the standard conforming linear finite element space based on body-fit partitions. Numerical examples of the related finite element method based on this IFE space are provided.

KW - Error estimates

KW - Finite element

KW - Immersed interface

KW - Interface problems

UR - http://www.scopus.com/inward/record.url?scp=2342455894&partnerID=8YFLogxK

U2 - 10.1002/num.10092

DO - 10.1002/num.10092

M3 - Journal article

SN - 0749-159X

VL - 20

SP - 338

EP - 367

JO - Numerical Methods for Partial Differential Equations

JF - Numerical Methods for Partial Differential Equations

IS - 3

ER -

An Immersed Finite Element Space and Its Approximation Capability

Abstract

Keywords

ASJC Scopus subject areas

More information

Other files and links

Fingerprint

Cite this