Phd Students (Status: Completed)
Sumit Mahajan (After completing his PhD, he joined INRIA Lille as a postdoctoral fellow. )
Finite element approximation for a delayed generalized Burgers-Huxley equation with weakly singular kernels: Part I Well-posedness, Regularity and Conforming approximation,
Computer & Mathematics with applications, 174 (2024), 261-286. [Arxiv Preprint][link]
Finite element approximation for the delayed generalized Burgers-Huxley equation with weakly singular kernel: Part II Non-Conforming and DG approximation,
SIAM Journal on Scientific Computing (SISC), 46 (5), (2024), A2972-A2998. [Arxiv Preprint][link]
A posteriori error estimates for the Generalized Burgers-Huxley equation with weakly singular kernels
Accepted, IMA Journal of Numerical Analysis, 2025. [Arxiv Preprint]
hp- discontinuous Galerkin method for the Generalized Burgers-Huxley equation with weakly singular kernels
Under Revision. [Arxiv Preprint]
Dynamic output-based feedback stabilizability for linear parabolic equations with memory
Under Revision [Arxiv Preprint]
Phd Students (Status: In progress)
Harpal Singh
SIAM Journal on Scientific Computing (SISC), 47 (2), (2025), A1251-A1278. [Arxiv Preprint]
Conforming/Non-conforming mixed finite element methods for optimal control of velocity-vorticity-pressure formulation for the oseen problem with variable viscosity
Accepted, Computer & Mathematics with Applications, 2025. [Arxiv Preprint]
Adaptive Embedded DG Methods for Optimal Control of Oseen Equation
Under Review
C^1 Virtual Element Methods for the Optimal Control of Oseen Equations with Stream-Function Formulation
Under Review
Shiv Mishra
Consistent PINNs for Fourth order elliptic PDEs
Under Review
A priori error analysis of consistent PINNs for parabolic PDEs
Under Review [Arxiv Preprint]
Ajay Kumar
Postdoc Fellows (Former)
Jai Tushar (He is currently working as a postdoctoral fellow at Monash University, Australia.)
Non-Conforming Structure Preserving Finite Element Method for Doubly Diffusive Flows on Bounded Lipschitz Domains
Under Review. [Arxiv Preprint]
Optimal Control of Stationary Doubly Diffusive Flows on Lipschitz Domains
Under Review. [Arxiv Preprint]
Mahendranath Perisetthi (He is currently working as a postdoctoral fellow at the Czech Academy of Sciences, Prague.)