No abstract

We analyze an immersed interface finite element method based on linear polynomials on noninterface triangular elements and piecewise linear polynomials on interface triangular elements. The flux jump condition is weakly enforced on the smooth interface. Optimal error estimates are derived in the broken H 1 -norm and L 2 -norm.

Abstract. The object of this note is to correct an error in the proof of Theorem 3.4 of the paper [An analysis of a broken P 1 -nonconforming finite element method for interface problems, SIAM J. Numer. Anal., 48 (2010), pp. 2117-2134]. As a result, Theorem 3.4 requires a higher regularity than the usual elliptic interface problems can have, i.e., β∇p ∈ H 1/2+ (Ω) 2 (0 < < 1/2). Hence we point out that even though the result now holds under this extra regularity assumption, the regularity is unlikely to hold for general interface problems. Thus the result has some limited usage.