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
Accepted, IMA Journal of Numerical Analysis, 2026. [Arxiv Preprint]
Dynamic output-based feedback stabilizability for linear parabolic equations with memory
Accepted, ESAIM Mathematical Modelling and Numerical analysis (ESAIM: M2AN), 2026. [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 Revision
C^1 Virtual Element Methods for the Optimal Control of Oseen Equations with Stream-Function Formulation
Under Revision
PRIMAL AND MIXED LOCKING–FREE NON–CONFORMING VIRTUAL ELEMENT METHODS FOR CONTROL CONSTRAINED LINEAR ELASTICITY EQUATIONS
Under Review
Structure-preserving $H(\mathrm{div})$-conforming DG and HDG methods for optimal control of linear elasticity
Under Review
Shiv Mishra
Mixed Consistent PINNs for Elliptic Obstacle Problems with Stability Analysis
Under Review
Consistent PINNs for Higher order elliptic PDEs
Accepted, International journal for numerical methods in engineering (IJNME), 2026.
A priori error analysis of consistent PINNs for parabolic PDEs
Under Review [Arxiv Preprint]
Ajay Kumar
Avnish Kumar
Postdoc Fellows (Former)
Jai Tushar (He is currently working as a postdoctoral fellow at Louisiana State University, USA.)
Non-Conforming Structure Preserving Finite Element Method for Doubly Diffusive Flows on Bounded Lipschitz Domains
Under Revision. [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.)