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

TitleA robust Nitsche's formulation for interface problems with spline-based finite elements
Publication TypeJournal Article
Year of Publication2015
AuthorsW Jiang, C Annavarapu, JE Dolbow, and I Harari
JournalInternational Journal for Numerical Methods in Engineering
Volume104
Start Page676
Issue7
Pagination676 - 696
Date Published11/2015
Abstract

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.

DOI10.1002/nme.4766
Short TitleInternational Journal for Numerical Methods in Engineering