**
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.
**

by J. T. Beale, D. L. Chopp, R. J. LeVeque, and Zhilin Li
*Comm. Appl. Math. Comput. Sci.* 3 (2008), pp. 95-100.

**Abstract.**
A recent paper by Vaughan, Smith, and Chopp
[Comm. App. Math. & Comp. Sci. 1 (2006), 207228]
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.

**Keywords.**
immersed interface method (IIM), elliptic
interface problems, finite difference methods, discontinuous coefficients,
singular source term, convergence order

**AMS(MOS) Subject Classifications.**
Primary: 65N06, 65N30, 65N50

**bibtex entry:**

@article{be-ch-le-li:camcos08, author="J. T. Beale and D. L. Chopp and R. J. LeVeque and Z. Li ", 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.", journal="Comm. Appl. Math. Comput. Sci.", volume="3", year="2008", pages="95-100" }