Journals (In review/In revision)
A. Khan, D. Mora, A. Silgado, H. Singh
C^1 Virtual Element Methods for the Optimal Control of Oseen Equations with Stream-Function Formulation
Under Review
S. Mishra, A. Khan
Consistent PINNs for H order elliptic PDEs
Under Review
S. Mishra, A. Khan
A priori error analysis of consistent PINNs for parabolic PDEs
Under Review [Arxiv Preprint]
Harpal Singh, Arbaz Khan
Adaptive Embedded DG Methods for Optimal Control of Oseen Equations
Under Review
Arbaz Khan, David Mora, Ricardo Ruíz-Baier, Jesus Vellojin
Divergence conforming finite element methods for flow-transport coupling with osmotic effects
Under Review. [Arxiv Preprint]
Jai Tushar, Arbaz Khan, Manil T Mohan
Non-Conforming Structure Preserving Finite Element Method for Doubly Diffusive Flows on Bounded Lipschitz Domains
Under Review. [Arxiv Preprint]
A Khan, F Lepe, D Mora, J Vellojin
Finite element analysis of the nearly incompressible linear elasticity eigenvalue problem with variable coefficients
Under Review [Arxiv Preprint]
Jai Tushar, Arbaz Khan, Manil T Mohan
Optimal Control of Stationary Doubly Diffusive Flows on Lipschitz Domains
Under Review. [Arxiv Preprint]
A. Khan, S. Mahajan, S. Rodrigues
Dynamic output-based feedback stabilizability for linear parabolic equations with memory
Under Revision [Arxiv Preprint]
Sumit Mahajan, Arbaz Khan
hp- discontinuous Galerkin method for the Generalized Burgers-Huxley equation with weakly singular kernels
Under Revision. [Arxiv Preprint]
Journal (Published/Accepted)
A Khan, F Lepe, J Vellojin
Accepted, SIAM Journal on Scientific Computing (SISC), 2025. [Arxiv Preprint]
A. Khan, B. P. Lamichhane, R. Ruiz-Baier, and S. Villa-Fuentes
A priori and a posteriori error bounds for the fully mixed FEM formulation of poroelasticity with stress-dependent permeability
Accepted, IMA Journal of Numerical Analysis, 2025. [Arxiv Preprint]
D. Boffi, A. Khan
Adaptive Mixed FEM for the Stokes eigenvalue problem
Accepted, Mathematics of Computation (AMS), 2025. [Arxiv Preprint]
Sumit Mahajan, Arbaz Khan
A posteriori error estimates for the Generalized Burgers-Huxley equation with weakly singular kernels
Accepted, IMA Journal of Numerical Analysis, 2025. [Arxiv Preprint]
Harpal Singh, Arbaz Khan
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]
Harpal Singh, Arbaz Khan
SIAM Journal on Scientific Computing (SISC), 47 (2), (2025), A1251-A1278. [Arxiv Preprint]
Sumit Mahajan, Arbaz Khan
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]
Sumit Mahajan, Arbaz Khan, Manil T Mohan
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]
Sanuwar Ahmed Choudhury, N Kishore Kumar, Pankaj Biswas, Arbaz Khan
Nonconforming spectral element approximation for parabolic PDE with corner singularity
Computer & Mathematics with Applications, 147, 54-73, 2024. [link]
Santiago Badia, Martin Hornkjøl, Arbaz Khan, Kent-Andr\'e Mardal, Alberto F. Martín, Ricardo Ruiz-Baier
Efficient and reliable divergence-conforming methods for an elasticity-poroelasticity interface problem
Computer & Mathematics with applications, 157 (2024), 173-194 . [Arxiv Preprint][link]
Raimund Bürger, Arbaz Khan, Paul E. Méndez, Ricardo Ruiz-Baier
Divergence-conforming methods for transient doubly-diffusive flows: A priori and a posteriori error analysis
IMA Journal of Numerical Analysis, 44 (6) (2024), 3520-3572. [Arxiv Preprint][link]
Veronica Anaya, Arbaz Khan, David Mora, Ricardo Ruiz-Baier
Robust a posteriori error analysis for rotation-based formulations of the elasticity/poroelasticity coupling
SIAM Journal on Scientific Computing (SISC), 44(4), (2022), B964-B995. [Arxiv Preprint][link]
Arbaz Khan, Manil T Mohan, Ricardo Ruiz-Baier
Conforming, nonconforming and DG methods for the stationary generalized Burgers- Huxley equation
Journal of Scientific Computing, 88, 52 (2021). [Arxiv Preprint]
Arbaz Khan, Pietro Zanotti,
A nonsymmetric approach and a quasi-optimal and robust discretization for the Biot's model. Part I--Theoretical aspects
Mathematics of Computation (American Mathematical Society), 93 (335), 2022, 1143-1170. [Arxiv Preprint]
Arbaz Khan, David J. Silvester
Robust a posteriori error estimation for mixed finite element approximation of linear poroelasticity
IMA Journal of Numerical Analysis 41(3), 2021, 2000-2025.
Arbaz Khan, Catherine E. Powell
Parameter-robust Stochastic Galerkin mixed approximation for linear poroelasticity with uncertain inputs
SIAM Journal on Scientific Computing (SISC), 43(4), 2021, B855-B883. [Arxiv Preprint]
Arbaz Khan, Alex Bespalov, Catherine E. Powell, David J. Silvester
Robust a posteriori error estimation for stochastic Galerkin formulations of parameter-dependent linear elasticity equations
Mathematics of computation (American Mathematical Society), 90 (2021), 613-636. [Arxiv Preprint] [link]
Joscha Gedicke, Arbaz Khan
Divergence-conforming discontinuous Galerkin finite elements for Stokes eigenvalue problems
Numerishe Mathematik, 144, (2020), 585-614. [Arxiv Preprint][link]
Arbaz Khan
Spectral method and spectral element method for three dimensional linear elliptic system: analysis and application
Journal of Scientific Computing, 82, 40, (2020), 1-32. [link]
Arbaz Khan, Guido Kanschat
A robust a posteriori error estimator for Divergence-conforming DG methods for Oseen equation
SIAM Journal on Numerical Analysis (SINUM), 58(1), ( 2020), 492-518. [link]
Manil T Mohan, Arbaz Khan
On the generalized Burgers-Huxley equation: Existence, uniqueness, regularity, global attractors and numerical studies,
Discrete & Continuous Dynamical Systems - B, 2020. [link]
Arbaz Khan, Catherine E. Powell, David J. Silvester
Robust Error Estimation for Lowest-Order Approximation of Nearly Incompressible Elasticity
International Journal for Numerical Methods in Engineering (IJNME), 119, (2019), 18-37, [Arxiv Preprint ] [link]
Arbaz Khan, Catherine E. Powell, David J. Silvester
Robust Preconditioning for stochastic Galerkin formulations of parameter-dependent linear elasticity equations
SIAM Journal on Scientific Computing (SISC), 41(1), (2019), A402-A422 [Arxiv Preprint][link]
J. Gedicke, A. Khan
Arnold-Winther Mixed Finite Elements for Stokes Eigenvalue Problems
SIAM Journal on Scientific Computing (SISC), 40(5), (2018), A3449-A3469 [MIMSPreprint] [Arxiv Preprint] [link]
Arbaz Khan, C. S. Upadhyay, M. I. Gerristma
Spectral element method for parabolic interface problems
Computer Methods in Applied Mechanics and Engineering (CMAME) 317 (2018), 66-94. [MIMSPreprint] [link]
Arbaz Khan, P. Dutt, C. S. Upadhyay
Spectral Element Method for parabolic initial value problem with non-smooth data: analysis and application
Journal of Scientific Computing, 73 (2-3),(2017), 876-905. [link]
Akhlaq Hussain, Arbaz Khan
Least-squares spectral element preconditioners for fourth order elliptic problems
Computers and Mathematics with Applications, 74(3), (2017), 482-503. [link]
Arbaz Khan, Akhlaq Hussain, Subhashree Mohapatra, C. S. Upadhyay
Spectral Element Method for Three Dimensional Elliptic Problems with Smooth Interfaces
Computer Methods in Applied Mechanics and Engineering (CMAME) 315 (2017), 522-549. [link]
Arbaz Khan, Akhlaq Hussain
Exponentially accurate spectral element method for fourth order elliptic problems
Journal of Scientific Computing, 71(1), (2017), 303-328. [link]
Arbaz Khan, C. S. Upadhyay
Exponentially accurate nonconforming least-squares spectral element method for elliptic problems on unbounded domains
Computer Methods in Applied Mechanics and Engineering (CMAME) 305, (2016), 607-633. [link]
Arbaz Khan, P. Dutt, C. S. Upadhyay
Nonconforming Least-Squares Spectral Element Method for European options
Computers and Mathematics with Applications 70 (1), (2015), 47-65. [link]
Pardeep Kumar, Arbaz Khan, Debabrata Goswami
Importance of Molecular Heat Convection in Time Resolved Thermal Lens Study of Highly Absorbing Samples
Chemical Physics, 441 (2014), 5-10. [link]
F. Bertrand, D. Boffi, J. Gedicke, A. Khan,
Some remarks on the a posteriori error analysis of the mixed Laplace eigenvalue problem,
14th WCCM-ECCOMAS Congress, 2020. [link]
J. Gedicke, A. Khan
Adaptive finite element methods for Stokes eigenvalue problems
In Self-Adaptive Numerical Methods for Computationally Challenging Problems, Oberwolfach Rep., 13(3), (2016), 2420-2421. [link]