Research Interest:

Numerical Analysis, Finite Element Methods, Optimization, Optimal Control Problems, Partial Differential Equations(PDEs), Deep Learning for.     PDEs and Optimal Control Problems. 

Research Funding:

DST INSPIRE Faculty Fellowship (2025–2030): Received a research grant of Rs. 35 lakh for a period of five years under the Department of Science and Technology (DST), Government of India.

Grant No.: DST/INSPIRE/04/2024/004854.

 Publications/Preprints(in reverse chronological order):

• Ramesh Ch. Sau, Jing Li, Xindi Hu, Zhi Zhou, and Bangti Jin.  An Adaptive Error Estimator for Stationary Navier-Stokes Equation Using Variational Physics Informed Neural Networks (in preparation).

• Gouranga Mallik and Ramesh Chandra Sau.  An Error Analysis of Second Order Elliptic Optimal Control Problem via Hybrid Higher Order Methods.

• Ramesh Ch. Sau and Luowei Yin.  A Review of Neural Network Solvers for Second-order Boundary Value Problems.

• Yongcheng Dai, Bangti Jin, Ramesh Ch Sau, and Zhi Zhou. Solving Elliptic Optimal Control Problems via Neural Networks and Optimality System. Adv. Comput. Math. 51, 31 (2025).

• Thirupathi Gudi and Ramesh Ch. Sau.  A two-grid Adaptive Finite Element Method for the Dirichlet Boundary Control Problem Governed by Stokes Equation. 

• Jai Tushar, Ramesh Ch. Sau, and Anil Kumar.  Virtual Element Method for Control Constrained Dirichlet Boundary Control Problem Governed by Diffusion Problem.  Journal of Scientific Computing (2024) 98:21.

• Thirupathi Gudi and Ramesh Ch. Sau.  A  Two Level Finite Element Method for Stokes Constrained Dirichlet Boundary Control Problem.  Computers and Mathematics with Applications 129 (2023), 126-135.

• Thirupathi Gudi, Gouranga Mallik and Ramesh Ch. Sau.  Finite Element Analysis of Dirichlet Boundary Control Problem Governed by Linear Parabolic Equation. SIAM J. Control and Optim. 60(6)(2022), 3262-3288.

• Thirupathi Gudi and Ramesh Ch. Sau.  Finite Element Analysis of the Constrained Dirichlet Boundary Control Problem Governed by the Diffusion Problem. ESAIM Control Optim. Calc. Var. 26 (2020), Paper No. 78, 19 pp.

• Md Yasir Feroz Khan, Rahul Biswas and Ramesh Ch. Sau. Instability of Lagrange Interpolation on $H^1(\Omega)\cap\C(\bar{Omega})$. Math. Student 88 (2019), no. 1-2, 153-158.

• Asha K. Dond, Thirupathi Gudi, and Ramesh Ch. Sau.  An Error Analysis of Discontinuous Finite Element Methods for the Optimal Control Problems Governed by Stokes Equation.  Numer. Funct. Anal. Optim., 40 (2019), pp. 421-460. 

Here are my M.S. thesis and Ph.D. thesis.