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CONTACT INFORMATION:

Department of Mathematical Science,

Room 318 Bell Hall Bldg,

University of Texas at El Paso, El Paso.

email address : nssharma@utep.edu

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Welcome to my webpage!

About me:

  • I am currently a tenure track assistant professor at Department of Mathematical Sciences, at UTEP.

  • Till Fall 2014, I was a post doctoral fellow in the working group Mathematical Methods of Simulation headed by Prof. Guido Kanschat , University of Heidelberg, Heidelberg, Germany.

  • In December 2011, I completed my Ph.D. from the University of Houston, Houston Texas under the guidance of Prof. Ronald Hoppe.

  • Prior to my time in Houston, I obtained my Bachelors and Masters in Mathematics from the University of Delhi, New Delhi, India.

    • Research Interests:

    My research interests lie in the field of Applied Mathematics and Scientific Computing with an emphasis on applications in material sciences and computational mechanics. Specifically, my focus is on using the discontinuous Galerkin method and the C0 interior penalty framework to solve problems often times relying on adaptively refined meshes or time-step adaptivity.

    External Funding  NSF DMS 1520862: Collaborative Research: Numerical Simulation of the Morphosynthesis of Polycrystalline Biominerals, 2015-2018; PI (with PI at participating institute Ronald Hoppe, University of Houston)

    Publications

  • N. S. Sharma and G. Kanschat, A Contraction Property of an Adaptive Divergence-Conforming Discontinuous Galerkin Method for the Stokes Problem, Journal of Numerical Mathematics, 26(4), pp. 209-232, 2018.

  • S. Brenner, M. Oh, S. Pollock, K. Porwal, M. Schedensack, N. Sharma, A C0 interior penalty method for elliptic distributed optimal control problems in three dimensions with pointwise state constraints, Topics in Numerical Partial Differential Equations and Scientific Computing, IMA Volumes in Mathematics and Its Applications, 160, 2016.

  • Guido Kanschat and Natasha Sharma, Divergence-conforming Discontinuous Galerkin Methods and C0 Interior Penalty Methods, SIAM, Journal of Numerical Analysis, Vol. 52, Issue 4

  • R.H.W. Hoppe. and N. Sharma, Convergence Analysis of an Adaptive Interior Penalty Discontinuous Galerkin Method for the Helmholtz Equation, IMA Journal of Numerical Analysis,Volume 33, Issue 3, 2013.

  • C. Carstensen, R.H.W. Hoppe, N. Sharma and T. Warburton, Adaptive hybridized Interior Penalty Discontinuous Galerkin methods for H(curl)-elliptic problems. Numer. Math. Theor. Meth. Appl. 4, 13--37, 2011.

    Manuscripts Submitted

  • A. E. Diegel and N. Sharma, A C0 Interior Penalty Method for the Phase Field Crystal Equation. Link
  • N. Sharma, Robust a-posteriori error estimates for weak Galerkin method for the convection-diffusion problem. Link

    Conference Proceedings

  • N.S Sharma (Joint work with R.H.W Hoppe). Convergence Analysis of an Adaptive Interior Penalty Discontinuous Galerkin Method for the Helmholtz Equation. Oberwolfach Reports, Workshop on Theory and Applications of Discontinuous Galerkin Methods, 2012.

  • N.S Sharma (Joint work with Dr. R.H.W Hoppe and Dr. Tim Warburton). A posteriori error analysis for hybridized Interior Penalty Discontinuous Galerkin Method for H(curl)-elliptic problems. Oberwolfach Reports, Workshop on Computational Electromagnetism and Acoustics, Springer, Berlin-Heidelberg-New York 2010.