TY - JOUR
T1 - Correction
T2 - 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 [COMM. APP. MATH. AND COMP. SCI, 1, 1, (2006) (207-228)]
AU - Beale, J. Thomas
AU - Chopp, David L.
AU - Leveque, Randall J.
AU - Li, Zhilin
PY - 2008
Y1 - 2008
N2 - 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 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.
AB - 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 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.
KW - Convergence order
KW - Discontinuous coefficients
KW - Elliptic interface problems
KW - Finite difference methods
KW - Immersed interface method (IIM)
KW - Singular source term
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U2 - 10.2140/camcos.2008.3.95
DO - 10.2140/camcos.2008.3.95
M3 - Comment/debate
AN - SCOPUS:64049089954
SN - 1559-3940
VL - 3
SP - 95
EP - 100
JO - Communications in Applied Mathematics and Computational Science
JF - Communications in Applied Mathematics and Computational Science
IS - 1
ER -