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.

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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.

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dc.contributor.author Beale, J. T. (John Thomas), 1947- en_US
dc.contributor.author Chopp, David L. en_US
dc.contributor.author LeVeque, Randall J., 1955- en_US
dc.contributor.author Li, Zhilin, 1956- en_US
dc.date.accessioned 2009-05-20T21:36:28Z
dc.date.available 2009-05-20T21:36:28Z
dc.date.issued 2008 en_US
dc.identifier.citation COMM. APP. MATH. AND COMP. SCI., Vol. 3, No. 1, 2008 en_US
dc.identifier.uri http://pjm.math.berkeley.edu/camcos/2008/3-1/p05.xhtml en_US
dc.identifier.uri http://hdl.handle.net/1773/4637
dc.description.abstract A recent paper by Vaughan, Smith, and Chopp [Comm. App. Math. &and 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 XFEM 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. en_US
dc.description.sponsorship The work of Beale and Li was supported by the Program on Random Media at S.A.M.S.I. en_US
dc.language.iso en_US en_US
dc.rights Copyright @ 2008 Mathematical Sciences Publishers en_US
dc.subject immersed interface method (IIM) en_US
dc.subject elliptic interface problems en_US
dc.subject finite difference methods en_US
dc.subject discontinuous coefficients en_US
dc.subject singular source term en_US
dc.subject convergence order en_US
dc.title 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. en_US
dc.type Article en_US


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