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.

摘要

A recent paperby Vaughan, Smith, and Chopp [Comm. App. Math. &and Comp. Sci.1 (2006), 207–228] reported numerical results for threeexamples using the immersed interface method (IIM) and the extendedfinite element method (X-FEM). The results presented for the IIMshowed first-order accuracy for the solution and inaccurate valuesof the normal derivative at the interface. This was due to an errorin the implementation. The purpose of this note is to presentcorrect results using the IIM for the same examples used in thatpaper, which demonstrate the expected second-order accuracy in themaximum norm over all grid points. Results now indicate that onthese problems the IIM and XFEM methods give comparable accuracy insolution values. With appropriate interpolation it is also possibleto obtain nearly second order accurate values of the solution andnormal derivative at the interface with the IIM.