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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:

  • a posteriori error analysis for partial differential equations discretized through Galerkin methods.
  • exploring new applications of finite exterior calculus.
  • Analysis of non linear partial differential equations specifically p-Biharmonic, p-Laplacian problems.

    For more details of my past work, click here.

  • 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

  • A $C^0$ Interior Penalty Method for elliptic distributed Optimal Control Problems in three dimensions with pointwise state Constraints. S.Brenner, M.Oh. S.Pollock, K.Porwal, M.Schedensack and N.Sharma.(submitted)
  • Guido Kanschat and Natasha Sharma, Divergence-conforming Discontinuous Galerkin Methods and $C^0$ 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, 2014).

  • 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.

    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.

    Preprints

  • Natasha Sharma and Guido Kanschat, Convergence of an adaptive Divergence-conforming Discontinuous Galerkin Method for the Stokes Problem, (in preparation).
  • D. Braess, R.H.W. Hoppe, N. S. Sharma, The Hypercircle Method and an equilibrated a posteriori error estimator for Discontinuous Galerkin approximations of elliptic boundary value problems on Quadilateral Meshes.