Research Interests
Numerical Solution of Partial Differential Equations, Numerical Linear Algebra, Discontinuous Galerkin (DG) FEM, HDG FEM, A Posteriori Error Analysis
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Research
Optimal Control of Stationary Doubly Diffusive Flows on Two and Three Dimensional Bounded Lipschitz Domains: A Theoretical Study
2023
Jai Tushar, Arbaz Khan, Manil T Mohan | arXiv:2308.02178
Journal: Arxiv Preprint
Finite element approximation for the delayed generalized Burgers-Huxley equation with weakly singular kernel: Part II Non-Conforming and DG approximation
2024
Sumit Mahajan, Arbaz Khan | SIAM
Journal: SIAM Journal on Scientific Computing (SISC)
Finite element approximation for a delayed generalized Burgers-Huxley equation with weakly singular kernels: Part I Well-posedness, Regularity and Conforming approximation
2023
Sumit Mahajan, Arbaz Khan, Manil T Mohan | arXiv:2309.01636
Journal: Arxiv Preprint
Nonconforming spectral element approximation for parabolic PDE with corner singularity
2024
Sanuwar Ahmed Choudhury, N Kishore Kumar, Pankaj Biswas, Arbaz Khan | Elsevier
Journal: Computer & Mathematics with Applications Pages: 54-73 , Volumes: 147 ,
Efficient and reliable divergence-conforming methods for an elasticity-poroelasticity interface problem
2024
Santiago Badia, Martin Hornkjøl, Arbaz Khan, Kent-Andr\'e Mardal, Alberto F. MartÃn, Ricardo Ruiz-Baier | Computer & Mathematics with applications,
Journal: Elsevier Pages: 173-194 , Volumes: 157 ,
Finite element analysis of the nearly incompressible linear elasticity eigenvalue problem with variable coefficients
2024
A Khan, F Lepe, D Mora, J Vellojin | ArXiv Preprint
Journal: ArXiv:2312.10715
Adaptive Mixed FEM for the Stokes eigenvalue problem
2024
D. Boffi, A. Khan | ArXiv Preprint
Journal: arXiv:2401.07132
Optimal Control of Stationary Doubly Diffusive Flows on Two and Three Dimensional Bounded Lipschitz Domains: Numerical Analysis
2024
Jai Tushar, Arbaz Khan, Manil T Mohan | ArXiv Preprint
Journal: ArXiv:2403.10282
Interior penalty discontinuous Galerkin methods for the nearly incompressible elasticity eigenvalue problem with heterogeneous media
2024
A Khan, F Lepe, J Vellojin | ArXiv Preprint
Journal: ArXiv:2402.17711
Divergence conforming DG method for the optimal control of the Oseen equation with variable viscosity
2024
Harpal Singh, Arbaz Khan | ArXiv Preprint
Journal: SIAM Journal on Scientific Computing (SISC)
Conforming/Non-conforming mixed finite element methods for optimal control of velocity-vorticity-pressure formulation for the oseen problem with variable viscosity
2024
Harpal Singh, Arbaz Khan | ArXiv
Journal: ArXiv
A posteriori error estimates for the Generalized Burgers-Huxley equation with weakly singular kernels
2024
Sumit Mahajan, Arbaz Khan | ArXiv Preprint
Journal: ArXiv:2403.08269
Divergence conforming finite element methods for flow-transport coupling with osmotic effects
2024
Arbaz Khan, David Mora, Ricardo RuÃz-Baier, Jesus Vellojin | arXiv Preprint
Journal: ArXiv:2402.01451
Divergence-conforming methods for transient doubly-diffusive flows: A priori and a posteriori error analysis
2023
Raimund Bürger, Arbaz Khan, Paul E. Méndez, Ricardo Ruiz-Baier | Oxford Academics
Journal: IMA Journal of Numerical Analysis
Robust a posteriori error analysis for rotation-based formulations of the elasticity/poroelasticity coupling
2022
Veronica Anaya, Arbaz Khan, David Mora, Ricardo Ruiz-Baier | SIAM
Journal: SIAM Journal on Scientific Computing (SISC) Pages: 23 ,
Conforming, nonconforming and DG methods for the stationary generalized Burgers-Huxley equation
2021
A Khan, MT Mohan, R Ruiz-Baier | Springer
Journal: Journal of Scientific Computing Pages: 88 , Volumes: 52 ,
A nonsymmetric approach and a quasi-optimal and robust discretization for the Biot's model. Part I--Theoretical aspects
2022
Arbaz Khan, Pietro Zanotti | American Mathematical Society
Journal: Mathematics of Computation Pages: 1143-1170 , Volumes: 91 ,
Robust a posteriori error estimation for mixed finite element approximation of linear poroelsticity,
2021
A. Khan, D. J. Silvester | Oxford University Press
Journal: IMA Journal of Numerical Analysis Pages: 2000-2025 , Volumes: 41(3) ,
Parameter-robust stochastic Galerkin approxination for linear poroelasticity with uncertain inputs
2021
A. Khan, C. E. Powell | SIAM
Journal: SIAM Journal on Scientific Computing (SISC) Pages: B855-B883 , Volumes: 43(4) ,
Robust a posteriori error estimation for stochastic Galerkin formulations of parameter-dependent linear elasticity equations
2021
A. Khan, A. Bespalov, C. E. Powell, D. J. Silvester | American Mathematical Society
Journal: Mathematics of Computation Pages: 613-636 , Volumes: 90 ,
Divergence-conforming discontinuous Galerkin finite elements for Stokes eigenvalue problems
2020
J. Gedicke, A. Khan | Springer
Journal: Numerische Mathematik Pages: 585-614 , Volumes: 144 ,
Spectral method and spectral element method for three dimensional linear elliptic system: analysis and application
2020
A. Khan | Springer
Journal: Journal of Scientific Computing Pages: 1-32 , Volumes: 82 ,
A robust a posteriori error estimator for Divergence-conforming DG methods for Oseen equation
2020
A. Khan, G. Kanschat | SIAM
Journal: SIAM Journal on Numerical Analysis (SINUM) Pages: 492-518 , Volumes: 58(1) ,
On the generalized Burgers-Huxley equation: Existence, uniqueness, regularity, global attractors and numerical studies
2020
Manil T Mohan, Arbaz Khan | American Institute of Mathematical Sciences
Journal: Discrete & Continuous Dynamical Systems - B Pages: 46 ,
Robust A Posteriori Error Estimators for Mixed Approximation of Nearly Incompressible Elasticity
2019
A. Khan, C. E. Powell, D. J. Silvester | Wiley
Journal: International Journal for Numerical Methods in Engineering (IJNME) Pages: 18-37 , Volumes: 119 ,
Robust Preconditioning for stochastic Galerkin formulations of parameter-dependent linear elasticity equations
2019
A. Khan, C. E. Powell, D. J. Silvester, | SIAM
Journal: SIAM Journal on Scientific Computing (SISC) Pages: A402-A421 , Volumes: 41(1) ,
Arnold-Winther Mixed Finite Elements for Stokes Eigenvalue Problems
2018
J. Gedicke, A. Khan | SIAM
Journal: SIAM Journal on Scientific Computing (SISC) Pages: A3449-A3469. , Volumes: 40(5) ,
Spectral element method for parabolic interface problems
2018
A. Khan, C. S. Upadhyay, M. I. Gerristma | Elsevier
Journal: Computer Methods in Applied Mechanics and Engineering (CMAME) Pages: 66-94 , Volumes: 317 ,
Least-squares spectral element preconditioners for fourth order elliptic problems
2017
A. Hussain, A. Khan | Elsevier
Journal: Computers and Mathematics with Applications Pages: 482-503 , Volumes: 74(3) ,
Spectral Element Method for parabolic initial value problem with non-smooth data: analysis and application
2017
A. Khan, P. Dutt, C. S. Upadhyay | Springer
Journal: Journal of Scientific Computing Pages: 876-905 , Volumes: 73(2-3) ,
Spectral Element Method for Three Dimensional Elliptic Problems with Smooth Interfaces
2017
A. Khan, A. Hussain, S. Mohapatra, C. S. Upadhyay | Elsevier
Journal: Computer Methods in Applied Mechanics and Engineering (CMAME) Pages: 522-549 , Volumes: 315 ,
Exponentially accurate spectral element method for fourth order elliptic problems
2017
A. Khan, A. Hussain | Springer
Journal: Journal of Scientific Computing Pages: 303-328 , Volumes: 71(1) ,
Exponentially accurate nonconforming least-squares spectral element method for elliptic problems on unbounded domains
2016
A. Khan, C. S. Upadhyay | Elsevier
Journal: Computer Methods in Applied Mechanics and Engineering (CMAME) Pages: 607-633 , Volumes: 305 ,
Nonconforming Least-Squares Spectral Element Method for European options
2015
A. Khan, P. Dutt, C. S. Upadhyay | Elsevier
Journal: Computers and Mathematics with Applications Pages: 47-65 , Volumes: 70(1) ,
Importance of Molecular Heat Convection in Time Resolved Thermal Lens Study of Highly Absorbing Samples
2014
P. Kumar, A. Khan, D. Goswami | Elsevier
Journal: Chemical Physics Pages: 5-10 , Volumes: 441 ,
Honors And Awards
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