CORRECTION TO THE ARTICLE A COMPARISON OF THE EXTENDED FINITE ELEMENT METHOD WITH THE IMMERSED INTERFACE METHOD FOR ELLIPTIC EQUATIONS WITH DISCONTINUOUS COEFFICIENTS AND SINGULAR SOURCES BY VAUGHAN ET AL.

被引：3

作者：

Beale, J. Thomas ^{[1
]}

Chopp, David L. ^{[2
]}

Leveque, Randall J. ^{[3
]}

Li, Zhilin ^{[4
,5
]}

机构：

[1] Duke Univ, Dept Math, Durham, NC 27708 USA

[2] Northwestern Univ, Dept Engn Sci & Appl Math, Evanston, IL 60208 USA

[3] Univ Washington, Dept Appl Math, Seattle, WA 98195 USA

[4] N Carolina State Univ, Ctr Res Sci Computat, Raleigh, NC 27695 USA

[5] N Carolina State Univ, Dept Math, Raleigh, NC 27695 USA

来源：

COMMUNICATIONS IN APPLIED MATHEMATICS AND COMPUTATIONAL SCIENCE | 2008年 / 3卷 / 01期

关键词：

immersed interface method (IIM); elliptic interface problems; finite difference methods; discontinuous coefficients; singular source term; convergence order;

D O I：

10.2140/camcos.2008.3.95

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

A recent paper by Vaughan, Smith, and Chopp [Comm. App. Math. & Comp. Sci. 1 (2006), 207-228] reported numerical results for three examples using the immersed interface method (IIM) and the extended finite element method (X-FEM). The results presented for the IIM showed first-order accuracy for the solution and inaccurate values of the normal derivative at the interface. This was due to an error in the implementation. The purpose of this note is to present correct results using the IIM for the same examples used in that paper, which demonstrate the expected second-order accuracy in the maximum norm over all grid points. Results now indicate that on these problems the IIM and X-FEM methods give comparable accuracy in solution values. With appropriate interpolation it is also possible to obtain nearly second order accurate values of the solution and normal derivative at the interface with the IIM.

引用

页码：95 / 100

页数：6

共 7 条

[1]

Beale JT., 2006, COMM APP MATH COM SC, V1, P91, DOI [10.2140/camcos.2006.1.91, DOI 10.2140/CAMCOS.2006.1.91]

[2] Convergence analysis of the immersed interface method [J].

Huang, HX ;

Li, ZL .

IMA JOURNAL OF NUMERICAL ANALYSIS, 1999, 19 (04) :583-608

[3] THE IMMERSED INTERFACE METHOD FOR ELLIPTIC-EQUATIONS WITH DISCONTINUOUS COEFFICIENTS AND SINGULAR SOURCES [J].

LEVEQUE, RJ ;

LI, ZL .

SIAM JOURNAL ON NUMERICAL ANALYSIS, 1994, 31 (04) :1019-1044

[4]

Li Z., 2006, FRONTIERS APPL MATH, V33

[5] Maximum principle preserving schemes for interface problems with discontinuous coefficients [J].

Li, ZL ;

Ito, K .

SIAM JOURNAL ON SCIENTIFIC COMPUTING, 2001, 23 (01) :339-361

[6]

Smith B. G., 2007, COMMUN APPL MATH COM, V2, P35, DOI [10.2140/camcos.2007.2.35, DOI 10.2140/CAMCOS.2007.2.35]

[7]

VAUGHAN BL, 2006, COMMUN APPL MATH COM, V1, P207

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