4 citations · 7 across the 15 of their papers we have counts for
17 papers
Divisibility Estimates for Gaussian Norms and Almost-Prime Orders of a CM Elliptic Curve
SeungJu Lee
Let . We prove that is squarefree and has at most two prime factors for primes . The proof follows the Gaussian CM sie…
A locking free mixed FEM based on a pure pseudostress based formulation for the elasticity eigenproblem
Arbaz Khan, Felipe Lepe, Jesus Vellojin
We analyze a novel locking-free mixed formulation for the elasticity eigenvalue problem in both two and three dimensions, expressed exclusively in terms of the pseudostress tensor.…
Nitsche-based FEM for the Laplace eigenvalue problem: spectral approximation and a posteriori error analysis
Arbaz Khan, David Mora, Jesus Vellojin
In this paper, we present the numerical analysis of an elliptic eigenvalue problem in which the essential boundary condition is imposed weakly by means of the Nitsche method. The r…
Finite element analysis for a Herrmann pressure formulation of the elastoacoustic problem with variable coefficients
Arbaz Khan, Felipe Lepe, David Mora +2
In two and three dimensions, this study is focused on the numerical analysis of an eigenproblem associated with a fluid-structure model for sloshing and elasto-acoustic vibration.…
Dynamic output-based feedback stabilizability for linear parabolic equations with memory
Arbaz Khan, Sumit Mahajan, Sérgio S. Rodrigues
The stabilizability of a general class of linear parabolic equations with a memory term, is achieve by explicit output feedback. The control input is given as a function of a state…
A priori and a posteriori error bounds for the fully mixed FEM formulation of poroelasticity with stress-dependent permeability
Arbaz Khan, Bishnu P. Lamichhane, Ricardo Ruiz-Baier +1
We develop a family of mixed finite element methods for a model of nonlinear poroelasticity where, thanks to a rewriting of the constitutive equations, the permeability depends on…
hp-discontinuous Galerkin method for the generalized Burgers-Huxley equation with weakly singular kernels
Sumit Mahajan, Arbaz Khan
In this work, we investigate the -discontinuous Galerkin (DG) time-stepping method for the generalized Burgers-Huxley equation with memory, a non-linear advection-diffusion-rea…
Conforming/Non-Conforming Mixed Finite Element Methods for Optimal Control of Velocity-Vorticity-Pressure Formulation for the Oseen Problem with Variable Viscosity
Harpal Singh, Arbaz Khan
This work examines the distributed optimal control of generalized Oseen equations with non-constant viscosity. We propose and analyze a new conforming augmented mixed finite elemen…
Divergence conforming DG method for the optimal control of the Oseen equation with variable viscosity
Harpal Singh, Arbaz Khan
This study introduces the divergence-conforming discontinuous Galerkin finite element method (DGFEM) for numerically approximating optimal control problems with distributed constra…
Non-Conforming Structure Preserving Finite Element Method for Doubly Diffusive Flows on Bounded Lipschitz Domains
Jai Tushar, Arbaz Khan, Manil T. Mohan
We study a stationary model of doubly diffusive flows with temperature-dependent viscosity on bounded Lipschitz domains in two and three dimensions. A new well-posedness and regula…
A posteriori error estimates for the Generalized Burgers-Huxley equation with weakly singular kernels
Sumit Mahajan, Arbaz Khan
This paper explores the residual based a posteriori error estimations for the generalized Burgers-Huxley equation (GBHE) featuring weakly singular kernels. Initially, we present a…
Interior penalty discontinuous Galerkin methods for the nearly incompressible elasticity eigenvalue problem with heterogeneous media
Arbaz Khan, Felipe Lepe, Jesus Vellojin
This paper studies the family of interior penalty discontinuous Galerkin methods for solving the Herrmann formulation of the linear elasticity eigenvalue problem in heterogeneous m…
Divergence conforming finite element methods for flow-transport coupling with osmotic effects
Arbaz Khan, David Mora, Ricardo Ruíz-Baier +1
We propose a model for the coupling of flow and transport equations with porous membrane-type conditions on part of the boundary. The governing equations consist of the incompressi…
Finite element analysis of the nearly incompressible linear elasticity eigenvalue problem with variable coefficients
Arbaz Khan, Felipe Lepe, David Mora +1
In this paper we present a mathematical and numerical analysis of an eigenvalue problem associated to the elasticity-Stokes equations stated in two and three dimensions. Both probl…
Finite element approximation for the delayed generalized Burgers-Huxley equation with weakly singular kernel: Part II Non-Conforming and DG approximation
Sumit Mahajan, Arbaz Khan
In this paper, the numerical approximation of the generalized Burgers'-Huxley equation (GBHE) with weakly singular kernels using non-conforming methods will be presented. Specifica…
Finite element approximation for a delayed generalized Burgers-Huxley equation with weakly singular kernels: Part I Well-posedness, Regularity and Conforming approximation
Sumit Mahajan, Arbaz Khan, Manil T. Mohan
The analysis of a delayed generalized Burgers-Huxley equation (a non-linear advection-diffusion-reaction problem) with weakly singular kernels is carried out in this work. Moreover…
A nonsymmetric approach and a quasi-optimal and robust discretization for the Biot's model. Part I -- Theoretical aspects
A. Khan, P. Zanotti
We consider the system of partial differential equations stemming from the time discretization of the two-field formulation of the Biot's model with the backward Euler scheme. A ty…