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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Date
2008Author
Beale, J. T.
(John Thomas), 1947-
Chopp, David
L.
LeVeque, Randall J
Li, Zhilin,
1956-
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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.