Skip to main content
Journal cover image

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

Publication ,  Journal Article
Jiang, W; Annavarapu, C; Dolbow, JE; Harari, I
Published in: International Journal for Numerical Methods in Engineering
November 16, 2015

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.

Duke Scholars

Published In

International Journal for Numerical Methods in Engineering

DOI

EISSN

1097-0207

ISSN

0029-5981

Publication Date

November 16, 2015

Volume

104

Issue

7

Start / End Page

676 / 696

Related Subject Headings

  • Applied Mathematics
  • 40 Engineering
  • 09 Engineering
 

Citation

APA
Chicago
ICMJE
MLA
NLM
Jiang, W., Annavarapu, C., Dolbow, J. E., & Harari, I. (2015). A robust Nitsche's formulation for interface problems with spline-based finite elements. International Journal for Numerical Methods in Engineering, 104(7), 676–696. https://doi.org/10.1002/nme.4766
Jiang, W., C. Annavarapu, J. E. Dolbow, and I. Harari. “A robust Nitsche's formulation for interface problems with spline-based finite elements.” International Journal for Numerical Methods in Engineering 104, no. 7 (November 16, 2015): 676–96. https://doi.org/10.1002/nme.4766.
Jiang W, Annavarapu C, Dolbow JE, Harari I. A robust Nitsche's formulation for interface problems with spline-based finite elements. International Journal for Numerical Methods in Engineering. 2015 Nov 16;104(7):676–96.
Jiang, W., et al. “A robust Nitsche's formulation for interface problems with spline-based finite elements.” International Journal for Numerical Methods in Engineering, vol. 104, no. 7, Nov. 2015, pp. 676–96. Scopus, doi:10.1002/nme.4766.
Jiang W, Annavarapu C, Dolbow JE, Harari I. A robust Nitsche's formulation for interface problems with spline-based finite elements. International Journal for Numerical Methods in Engineering. 2015 Nov 16;104(7):676–696.
Journal cover image

Published In

International Journal for Numerical Methods in Engineering

DOI

EISSN

1097-0207

ISSN

0029-5981

Publication Date

November 16, 2015

Volume

104

Issue

7

Start / End Page

676 / 696

Related Subject Headings

  • Applied Mathematics
  • 40 Engineering
  • 09 Engineering