मालवीय राष्ट्रीय प्रौद्योगिकी संस्थान जयपुर (राष्ट्रीय महत्व का संस्थान)
Malaviya National Institute of Technology Jaipur (An Institute of National Importance)
Department of Mathematics
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13

Journal Publications

4

Awards & Honours

Qualifications
  • Ph.D.(Mathematics) from IIT Guwahati(2019)
    M.Sc.(Mathematics) from IIT Kanpur(2012)
    B.Sc.(PCM) from C. S. J. M. University Kanpur(2010)
Research Interests

Optimal Control Problems, Conforming Finite Element Methods, Discontinuous Galerkin Methods, Mixed FEM, Adaptive method for PDEs, Computational method for linear/non-linear problems, Numerical evaluation and error estimation.

Professional Background
  • Assistant Professor at MNIT Jaipur [12 March 2026 - Present].
    DST Inspire Faculty Fellow at Indian Institute of Science, Bangalore [15 May 2024 - 06 March 2026].
    National Post Doctoral Fellow at Indian Institute of Science, Bangalore [07 March 2022 - 06 March 2024].
    Research Associate at IIT Delhi [01 April 2021 - 30 June 2021].
    Institute Post Doctoral Fellow at IIT Delhi [01 April 2019 - 31 March 2021].

    2026
  • P. Shakya and K. Porwal, "Adaptive finite element method for an elliptic optimal control problem with integral state constraints" , Communications on Applied Mathematics and Computation (Springer) Volume :8 / / 2026 DOI: https://doi.org/10.1007/s42967-024-00397-8
    • 2025
  • A. Pal, T. Gudi and P. Shakya,, "A $C^0$-IP method for distributed optimal control problem governed by a non-divergent form PDE with Cordes coefficients" , Mathematics of Computation (American Mathematical Society ) Volume :00 / / 2025 DOI: https://doi.org/10.1090/mcom/4109
    • 2024
  • P. Shakya, "Error analysis for parabolic optimal control problems with measure data in a nonconvex polygonal domain" , Journal of Computational Mathematics (Global Science Press) Volume :42 / 15791604 / 2024 DOI: https://doi.org/0.4208/jcm.2305-m2022-0215
  • P. Shakya, "Error analysis for the finite element approximations of Dirichlet parabolic boundary control problem with measure data" , Journal of mathematical analysis and applications (Elsevier) Volume :534 / / 2024 DOI: https://doi.org./10.1016/j.jmaa.2024.128109
  • T. Gudi and P. Shakya,, "Error estimates for a bubble-enriched $C^0$ interior penalty method to a reduced state constrained elliptic optimal control problem" , Journal of Computational and Applied Mathematics (Elsevier) Volume :460 / / 2024 DOI: https://doi.org/10.1016/j.cam.2024.116397
    • 2023
  • P. Shakya and R. K. Sinha, "Analysis for the space-time a posteriori error estimates for mixed finite element solutions of parabolic optimal control problems" , Numerical Algorithms (Springer ) Volume :96 / 879 - 924 / 2023 DOI: https://doi.org/10.1007/s11075-023-01669-9
    • 2021
  • K. Porwal and P. Shakya, "A finite element method for an elliptic optimal control problem with integral state constraints" , Applied Numerical Mathematics (Elsevier) Volume :169 / 273-288 / 2021 DOI: https://doi.org/10.1016/j.apnum.2021.07.002
  • P. Shakya and R. K. Sinha, "Finite element approximations of parabolic optimal control problem with measure data in time" , Applicable Analysis (Taylor and Francis) Volume :100 / 2706-2734 / 2021 DOI: https://doi.org/10.1080/00036811.2019.1698722
    • 2020
  • P. Shakya and R. K. Sinha, "Finite element method for parabolic optimal control problems with a bilinear state equation" , Journal of Computational and Applied Mathematics (Elsevier) Volume :367 / 112-431 / 2020 DOI: https://doi.org/10.1016/j.cam.2019.112431
  • P. Shakya and R. K. Sinha, "A priori error estimates for finite element discretizations of parabolic optimal control problems with measure data" , Numerical Functional Analysis and Optimization (Taylor & Francis) Volume :41 / 158-191 / 2020 DOI: https://doi.org/10.1080/01630563.2019.1615948
    • 2019
  • P. Shakya and R. K. Sinha, "A posteriori error analysis for finite element approximations of parabolic optimal control problems with measure data" , Applied Numerical Mathematics (Elsevier) Volume :136 / 23-45 / 2019 DOI: https://doi.org/10.1016/j.apnum.2018.09.015
  • P. Shakya and R. K. Sinha, "A priori and a posteriori error estimates of finite element approximations for elliptic optimal control problem with measure data" , Optimal Control Applications and Methods (John Wiley and Sons Ltd) Volume :40 / 241-264 / 2019 DOI: https://doi.org/10.1002/oca.2476
    • 2017
  • P. Shakya and R. K. Sinha, "A priori and a posteriori error estimates of $H^1$-Galerkin mixed finite element method for parabolic optimal control problems" , Optimal Control Applications and Methods (John Wiley and Sons Ltd) Volume :38 / 1056-1070 / 2017 DOI: https://doi.org/10.1002/oca.2312

  • International level Conference on Latest Advances in Computational and Applied Mathematics-2025(LACAM-25) at IISER Thiruvananthapuram, Thivandrum, India from 08-12-2025 to 11-12-2025
  • International level Conference on Inaugural meeting of Asian-Oceanian Women in Mathematics at International Center for Theoretical Sciences, Bangalore, India from 24-04-2023 to 28-04-2023
  • National level Conference on $37^{th}$ Annual Conference of Ramanujan Mathematical Society at SSN College of Engineering, Chennai, Chennai, India from 06-12-2022 to 08-12-2022
  • National level Conference on Partial Differential Equations and Numerical Analysis at Tata Institute of Fundamental Research, Bangalore, India from 28-04-2022 to 30-04-2022
  • International level Conference on International Conference on Advances in Differential Equations and Numerical Analysis at IIT Guwahati, Guwahati, India from 12-10-2020 to 15-10-2020
  • International level Workshop on Workshop on Finite Elements for Nonlinear and Multiscale Problems at Indian Institute of Science , Bangalore, India from 28-02-2020 to 03-03-2020
  • International level Conference on International Conference on Advances in Scientific Computing at IIT Madras, Chennai, India from 28-11-2016 to 30-11-2016
  • International level Workshop on CIMPA Summer School onCurrent Research in Finite Element Methods at IIT Bombay, Mumbai, India from 06-07-2015 to 17-07-2015
  • International level Workshop on Pre School for CIMPA School on Current Research in Finite Element Methods at IIT Bombay, Mumbai, India from 24-06-2015 to 04-07-2015
  • National level Workshop on Advanced Workshop on Hyperbolic PDEs: Theory, Numerics and Applications at LNM Institute of Information Technology, Jaipur, Jaipur, India from 01-12-2014 to 09-12-2014
  • National level Workshop on National Program on Differential Equations: Theory, Computations and Applications (NPDE-TCA) at IIT Guwahati, Guwahati, India from 02-06-2014 to 21-06-2014

  • DST INSPIRE Faculty Fellowship (20242029), for given by Department of Science and Technology (DST), Government of India Year - 2024
  • National Post-Doctoral Fellowship for given by Department of Science and Technology (DST), Government of India Year - 2021
  • Institute Post-Doctoral Fellowship for given by IIT Delhi Year - 2019
  • Merit-Cum-Means Scholarship (Under top 50 rank in Joint admission test for M.Sc) for given by IIT Kanpur Year - 2010