Erratum: An Analysis of a Broken P_1-Nonconforming Finite Element Method for Interface Problems

Abstract

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.

A Finite Difference Method for Two Dimensional Elliptic Interface Problems with Imperfect Contact

“…The discontinuity of solution is handled by incorporating the implicit jump conditions into a bilinear form through enriching usual P 1 finite element space by extra degrees of freedom on each side of the interface. Kwak and Lee [18] introduced a new variational form and a new finite element method for solving second-order elliptic interface problems where the jump of primary variable is related to the normal flux. The jump conditions along the interface is satisfied by modifying the P 1 -Crouzeix-Raviart element.…”