• Application of numerical methods to approximate solutions, eigenvalues and eigenvectors of elliptic PDEs
• Aspects of meshless methods and generalized finite element methods in the context of their approximation properties, error estimation schemes, and implementation
• Elliptic PDEs with non-smooth coefficients

• Robustness in stable generalized finite element methods (SGFEM) applied to crack problems (joint with Q. Zhang and I. Babuska)\
  submitted for publication.
• Stable Generalized Finite Element Method and associated iterative schemes; application to interface problems (joint with K. Kergrene and I. Babuska)
  submitted for publication.
• Stable GFEM (SGFEM): Improved conditioning and accuracy of GFEM/XFEM for three-dimensional fracture mechanics (joint with V. Gupta, I. Babuska, and C. A. Duarte)
  Comput. Methods Appl. Mech. Engrg. 2015, 289, 355-386-39, DOI 10.1016/j.cma.2015.01.014
• Higher order stable generalized finite element method (joint with Q. Zhang and I. Babuska)
  Numer. Math. 2014, 128, 1-29, DOI 10.1007/s00211-014-0609-1

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