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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.…
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…