Dr. Gautam Singh
Dr. Gautam Singh is an Assistant Professor of Mathematics in NIT Trichy since October 2022. His areas of research interest include Numerical Analysis, Finite Element Methods and Discontinuous Galerkin Methods. Previously he was an Assistant Professor in BIT Mesra from August 2021 to October 2022. He received his doctoral degree from IIT Guwahati in the year 2020 and the title of his thesis is “Superconvergence Analysis of the Discontinuous Galerkin Method for Singularly Perturbed Differential Equations”. He has completed his Masters from IIT Guwahati in 2015 and Bachelors in Mathematics from Banaras Hindu University in2013. He has cleared both GATE (rank-145) and NET (rank-47) in the year 2015. Other achievements of him include receiving Inspire Fellowship in 2015-2020 and Best Oral Presentation Award in 2018.
Education:
Research Areas:
Teaching/ Research Experience:
Ph.D. Students:
Courses Taught:
Fellowship/ Awards:
Recipient of Inspire Scholarship by the Department of Science and Technology, 2010-2015.
IIT Joint Admissions Test for M.Sc (JAM), January 2013, all India rank -173.
Graduate Aptitude Test in Engineering in Mathematics (GATE), Febuary 2015, all India Rank - 145.
UGC-CSIR NET in Mathematics, December 2015, all India Rank-47
Honored with the Best Oral Presentation Award at Research Conclave’18, IIT Guwahati.
Invited Talk:
Conferences:
NIPG method for two parameter singular perturbation problems. 2nd International Conference on Advance in Computational Mathematics (ICACM-2018) at Tribhuvan University, Kathmandu, Nepal.
Superconvergence properties of discontinuous Galerkin method with interior penalties for singularly perturbed problems. 34th Annual National Conference of BHU (NCMS-2019) at BHU Varanasi.
Superconvergence of discontinuous Galerkin method for non-stationary convection-diffusion reaction problems. Indo-German Conference on Computational Mathematics (IGCM 2019) at IISC, Bangalore.
Non symmetric discontinuous Galerkin method for fractional differential equations. The 10th International Congress on Indus- trial and Applied Mathematics (ICIAM 2023 Tokyo) at Waseda University, Tokyo, Japan .
Direct discontinuous Galerkin method for two parameter singular perturbation problems. 14th AIMS Conference on Dynamical systems and Differential Equations and Applications, United Arab Emirates (16 December, 2024 to 20 December, 2024).
Publication:
G. Singh and S. Natesan. Superconvergence of discontinuous Galerkin method with interior penalties for singularly perturbed two-point boundary-value problems. Calcolo, 55(4):54,2018.
G. Singh and S. Natesan. A uniformly convergent NIPG method for a singularly perturbed system of reaction-diffusion boundary-value problems. Springer Proc. Math. Stat., 253:429-440, 2018.
G. Singh and S. Natesan. Study of the NIPG method for two-parameter singular perturbation problems on several layer adapted grids. J. Appl. Math. Comput., 63(1–2):683-705, 2020.
G. Singh and S. Natesan. A uniformly convergent numerical scheme for a coupled system of singularly perturbed reaction- diffusion equations. Numer. Fun. Anal. Opt., 41(10):1172-1189, 2020.
M. K. Singh and G. Singh and S. Natesan. A unified study on superconvergence analysis of Galerkin FEM for singularly perturbed system of multi-scale nature. J. Appl. Math. Comput., 66:221-243, 2021.
A. Sendur, S. Natesan and G. Singh. Error estimates for a fully discrete ϵ-uniform finite element method on quasi uniform meshes. Hacettepe J. Math, Stat., 50(5):1306-1324, 2021.
G. Singh and S. Natesan. Superconvergence properties of discontinuous Galerkin time stepping for singularly perturbed parabolic problems. Numer. Algorithms.,90:1073-1090, 2022.
G. Singh, S. Natesan and A Sendur. Superconvergence error analysis of discontinuous Galerkin method with interior penalties for 2D elliptic convection-diffusion-reaction problems. International Journal of Computer Mathematics., 100(5):948-967, 2023.
A. Yadav and G. Singh. Analysis of two-parameter singular perturbation problems via the DDG method on Shishkin mesh. J. Appl. Math. Comput., https://link.springer.com/article/10.1007/s12190-025-02392-5, 2025.
V. Kumar and G. Singh. Discontinuous Galerkin Method for a Coupled System of Singularly Perturbed Convection-Diffusion Parabolic Partial Differential Equations. Numer. Algorithms., (Under Review), 2025.
A. Yadav and G. Singh. A Direct Discontinuous Galerkin Method for Efficiently Solving Singularly Perturbed Parabolic Equa- tions. Advances in Computational Mathematics, (Submitted), 2025.
Conatct:
Dr. Gautam Singh
Office No- 206, Lyceum Building
Assistant Professor, Department of Mathematics
NIT Trichy-620015, India
Email ID: gautam@nitt.edu, gautamsinghmath@gmail.com
Mobile no-04312503679, 09884987312
Research Gate:https://www.researchgate.net/profile/Gautam-Singh-28
Google Scholar: https://scholar.google.com/citations?user=8XYllKQAAAAJ&hl=en
Assistant Professor, Department of Mathematics
National Institute of Technology, Tiruchirappalli
Dr. Gautam Singh joined the Department of Mathematics, NIT Trichy, as an Assistant Professor in October 2022. His research expertise lies in Numerical Analysis, Finite Element Methods, Discontinuous Galerkin Methods, and Physics-Informed Neural Networks. With a strong academic and research background, his work focuses on developing efficient numerical schemes for singularly perturbed differential equations, multiscale problems, and PDEs with complex layer structures.
Prior to NIT Trichy, he served as an Assistant Professor at BIT Mesra (2021–2022) and worked as a Postdoctoral Fellow at IIT Roorkee (2021). Dr. Singh earned his Ph.D. from IIT Guwahati in 2020 under the guidance of Prof. Natesan Srinivasan, where he investigated superconvergence properties of discontinuous Galerkin methods. He received his M.Sc. in Mathematics and Computing from IIT Guwahati (2015) and B.Sc. (Hons.) in Mathematics from Banaras Hindu University (2013).
He qualified GATE (AIR 145) and CSIR-NET (AIR 47) in Mathematics in 2015. His achievements include the INSPIRE Fellowship (2015–2020) and the Best Oral Presentation Award at Research Conclave 2018, IIT Guwahati.
Ph.D., Applied Mathematics, IIT Guwahati (2015–2020)
M.Sc., Mathematics & Computing, IIT Guwahati (2013–2015)
B.Sc. (Hons.) Mathematics, Banaras Hindu University (2010–2013)
Numerical Analysis
Finite Element Methods
Discontinuous Galerkin Methods
Singular Perturbation Problems
Physics-Informed Neural Networks (PINNs)
Assistant Professor, Department of Mathematics, NIT Trichy (Oct 2022 – Present)
Assistant Professor, Department of Mathematics, BIT Mesra (Aug 2021 – Oct 2022)
Postdoctoral Fellow, IIT Roorkee (Feb 2021 – Aug 2021)
Amit Yadav (January 2023 – Present)
Vijay Kumar (January 2023 – Present)
Partial Differential Equations
Scientific Computing using Python
Programming in C (Lab)
Complex Analysis & Differential Equations
Fourier Transforms & Numerical Techniques
Linear Algebra & Calculus
Real Analysis & Probability Theory
INSPIRE Fellowship, DST (2015–2020)
IIT-JAM (AIR 173), 2013
GATE (AIR 145), Mathematics, 2015
CSIR-NET (AIR 47), Mathematics, 2015
Best Oral Presentation Award, Research Conclave 2018, IIT Guwahati
(You can share details here; I can format them beautifully.)
Presented research at ICMC-2018 (IIT BHU), ICACM-2018 (Kathmandu), NCMS-2019 (BHU)
Presented at IGCM 2019, IISc Bangalore
Delivered a talk at ICIAM 2023, Tokyo, Japan
Presented work at the AIMS Conference 2024, United Arab Emirates
(Formatted cleanly for homepage)
Superconvergence of DG method with interior penalties… Calcolo, 2018.
Uniformly convergent NIPG scheme for reaction–diffusion systems… Springer Proc. Math. Stat., 2018.
NIPG method for two-parameter SPPs… J. Appl. Math. Comput., 2020.
Coupled singularly perturbed systems… Numer. Funct. Anal. Optim., 2020.
Superconvergence analysis of Galerkin FEM… J. Appl. Math. Comput., 2021.
ε-uniform FEM on quasi-uniform meshes… Hacettepe J. Math. Stat., 2021.
DG time-stepping for singularly perturbed parabolic problems… Numer. Algorithms, 2022.
Superconvergence error analysis for 2D elliptic CDR problems… Int. J. Computer Mathematics, 2023.
DDG method for two-parameter SPPs… J. Appl. Math. Comput., 2025.
DG method for coupled convection–diffusion parabolic PDEs… Numer. Algorithms, Under Review, 2025.
Direct DG method for singularly perturbed parabolic equations… Adv. Comput. Math., Submitted, 2025.
Dr. Gautam Singh
Office No. 206, Lyceum Building
Department of Mathematics
NIT Tiruchirappalli – 620015, India
Email: gautam@nitt.edu, gautamsinghmath@gmail.com
Phone: 0431-2503679, +91-98849-87312
ResearchGate: https://www.researchgate.net/profile/Gautam-Singh-28
Google Scholar: https://scholar.google.com/citations?user=8XYllKQAAAAJ
