Department of Mathematics |
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Research: |
| I am a numerical analyst and I work on numerical solutions of partial differential equations. Currently, my research is foccused on Generalized Finite Element Methods and Meshless Methods. |
| Recent Publications |
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Approximation Properties of the Generalized Finite Element Method (joint with C. Anitescu) Submitted for publication, pdf |
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Effect of Numerical Integration on the Finite Element Approximation
of Linear Functionals (joint with I. Babuska, and Hengguang Li) Submitted for publication, pdf |
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Effect of Numerical Integration on Meshless Methods (joint with I. Babuska, J. E. Osborn, and Qinghui Zhang) Comput. Methods Appl. Mech. Engrg, 198 (2009) 2886-2897, pdf |
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Quadrature for Meshless Methods (joint with I. Babuska, J. E. Osborn, and Q> Li) Int. J. Numer. Meth. Engng., 2008, 76: 1434--1470, pdf |
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Superconvergence in Generalized Finite Element Method (joint with I. Babuska and J. E. Osborn) Numer. Math, 2007, 107: 353--395, pdf |
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Generalized Finite Element Method: Main Ideas, Results,
and Perspective (joint with I. Babuska and J. E. Osborn) International Journal of Computational Methods, Vol.1, No. 1, 2004, 67--103, pdf |
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On the Approximability and the Selection of Particle
Shape Functions (joint with I. Babuska and J. E. Osborn) Numer. Math., 2004, 96: 601--640, pdf |
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Survey of Meshless and Generalized Finite Element Methods: A Unified Approach (joint with I. Babuska and J. E. Osborn) Acta Numerica, 2003, 1--125, pdf |
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On Principles for the Selection of Shape Functions for the Generalized Finite Element Method (joint with I. Babuska and J. E. Osborn) Comput. Methods Appl. Mech. Engrg, 2002, 191, 5595--5629, pdf |