A robust Nitsche's formulation for interface problems with spline-based finite elements

Wen Jiang, Chandrasekhar Annavarapu, John E. Dolbow*, Isaac Harari

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


The extended finite element method (X-FEM) has proven to be an accurate, robust method for solving embedded interface problems. With a few exceptions, the X-FEM has mostly been used in conjunction with piecewise-linear shape functions and an associated piecewise-linear geometrical representation of interfaces. In the current work, the use of spline-based finite elements is examined along with a Nitsche technique for enforcing constraints on an embedded interface. To obtain optimal rates of convergence, we employ a hierarchical local refinement approach to improve the geometrical representation of curved interfaces. We further propose a novel weighting for the interfacial consistency terms arising in the Nitsche variational form with B-splines. A qualitative dependence between the weights and the stabilization parameters is established with additional element level eigenvalue calculations. An important consequence of this weighting is that the bulk as well as the interfacial fields remain well behaved in the presence of large heterogeneities as well as elements with arbitrarily small volume fractions. We demonstrate the accuracy and robustness of the proposed method through several numerical examples.

Original languageEnglish
Pages (from-to)676-696
Number of pages21
JournalInternational Journal for Numerical Methods in Engineering
Issue number7
StatePublished - 16 Nov 2015


  • B-splines
  • Embedded interface, stabilized
  • Nitsche's method
  • X-FEM


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