Dr Naresh Kumar

About

Hello, I'm Dr Naresh Kumar, currently an Assistant Professor at Dr B R Ambedkar National Institute of Technology Jalandhar, Punjab, India. I have obtained Ph.D. from the Indian Institute of Technology, Guwahati, in the Department of Mathematics.

My research interests include numerical methods for partial differential equations, and high-performance computing for FEMs with polygonal meshes. My Ph.D. dissertation was in the broad area of finite element methods for PDEs. More precisely, the work was on the Weak Galerkin finite element method for time-dependent problems on polygonal meshes. In my Postdoc at Indian Institute of Technology, Roorkee, we developed theoretical and numerical framework on weak Galerkin finite element approximations for singularly perturbed problems. In my second postdoc at Dongguan University of Technology China, we developed Hybrid High-Order method for nonlinear problems. In addition, Physics Informed Neural Networks (PINNs) are a recently proposed technique to solve Partial Differential Equations (PDEs), by exploiting the non-linearity and the approximation properties of neural networks. We are working in PINNS to predict the stabilization parameter in the WG stabilization technique for solving singularly perturbed differential equations (SPDEs). If you wish to chat with me about my research, feel free to mail me

Employment

• Dr. B. R. Ambedkar National Institute of Technology Jalandhar Assistant Professor
  2024 - Present
• Indian Institute of Technology Roorkee Postdoctoral Fellow
  2022 - 2023

Education

• Indian Institute of Technology Guwahati PhD
  2018 - 2022
• Indian Institute of Technology Bombay Master
  2015 - 2017
• Maharaja Ganga Singh University BSc
  2011 - 2015

Projects & Funding

Projects & funding information is unavailable.

Publications (14)

• High‐Order Weak Galerkin Finite Element Method for Analysis and Simulation of Nonlinear Wave Propagation in Homogeneous Media
  Numerical Methods for Partial Differential Equations 2026 DOI: 10.1002/num.70100
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• WG‐FEM With ADI‐Type Splitting: A High‐Order Approach for Two‐Parameter Singularly Perturbed 2D Parabolic Problems on Bakhvalov Mesh
  Numerical Methods for Partial Differential Equations 2025 DOI: 10.1002/num.70025
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• Weak Galerkin Finite Element Methods for Parabolic Problems With $L^2$ Initial Data
  International Journal of Numerical Analysis and Modeling 2023 DOI: 10.4208/ijnam2023-1009
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• A stabilizer free weak Galerkin finite element method for second‐order Sobolev equation
  Numerical Methods for Partial Differential Equations 2023 DOI: 10.1002/num.22960
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• A systematic study on weak Galerkin finite element method for second‐order parabolic problems
  Numerical Methods for Partial Differential Equations 2023 DOI: 10.1002/num.22973
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• Analysis and simulation of Korteweg-de Vries-Rosenau-regularised long-wave model via Galerkin finite element method
  Computers & Mathematics with Applications 2023 DOI: 10.1016/j.camwa.2023.01.027
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• Supercloseness analysis of a stabilizer free weak Galerkin finite element method for time dependent convection diffusion reaction equation
  Mathematics and Computers in Simulation 2023 DOI: 10.1016/j.matcom.2023.01.044
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• Supercloseness analysis of a stabilizer free weak Galerkin finite element methods for Viscoelastic Wave equation with variable coefficients
  Advances in Computational Mathematics 2023
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• A systematic study on weak Galerkin finite-element method for second-order wave equation
  Computational and Applied Mathematics 2022 DOI: 10.1007/s40314-022-02058-z
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• Developing Stabilizer Free Weak Galerkin finite element method for second-order wave equation
  Journal of Computational and Applied Mathematics 2022 DOI: 10.1016/j.cam.2022.114457
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