5 citations · 5 across the 8 of their papers we have counts for
12 papers
Efficient and reliable divergence-conforming methods for an elasticity-poroelasticity interface problem
S. Badia, M. Hornkjøl, A. Khan +3
We present a finite element discretisation to model the interaction between a poroelastic structure and an elastic medium. The consolidation problem considers fully coupled deforma…
Robust a posteriori error analysis for rotation-based formulations of the elasticity/poroelasticity coupling
VerÓnica Anaya, Arbaz Khan, David Mora +1
We develop the \textit{a posteriori} error analysis of three mixed finite element formulations for rotation-based equations in elasticity, poroelasticity, and interfacial elasticit…
Divergence-conforming methods for transient doubly-diffusive flows: A priori and a posteriori error analysis
Raimund Bürger, Arbaz Khan, Paul E. Méndez +1
The analysis of the double-diffusion model and -conforming method introduced in [Bürger, Méndez, Ruiz-Baier, SINUM (2019), 57:1318--1343] is extended to t…
Conforming, nonconforming and DG methods for the stationary generalized Burgers- Huxley equation
Arbaz Khan, Manil T Mohan, Ricardo Ruiz-Baier
In this work we address the analysis of the stationary generalized Burgers-Huxley equation (a nonlinear elliptic problem with anomalous advection) and propose conforming, nonconfor…
Parameter-robust Stochastic Galerkin mixed approximation for linear poroelasticity with uncertain inputs
Arbaz Khan, Catherine E. Powell
Linear poroelasticity models have a number of important applications in biology and geophysics. In particular, Biot's consolidation model is a well-known model that describes the c…
Robust a posteriori error estimation for stochastic Galerkin formulations of parameter-dependent linear elasticity equations
Arbaz Khan, Alex Bespalov, Catherine E. Powell +1
The focus of this work is a posteriori error estimation for stochastic Galerkin approximations of parameter-dependent linear elasticity equations. The starting point is a three-fie…
Divergence-conforming discontinuous Galerkin finite elements for Stokes eigenvalue problems
Joscha Gedicke, Arbaz Khan
In this paper, we present a divergence-conforming discontinuous Galerkin finite element method for Stokes eigenvalue problems. We prove a priori error estimates for the eigenvalue…
Robust preconditioning for stochastic Galerkin formulations of parameter-dependent nearly incompressible linear elasticity equations
Arbaz Khan, Catherine E. Powell, David J. Silvester
We consider the nearly incompressible linear elasticity problem with an uncertain spatially varying Young's modulus. The uncertainty is modelled with a finite set of parameters wit…
Robust error estimation for lowest-order approximation of nearly incompressible elasticity
Arbaz Khan, Catherine E. Powell, David J. Silvester
We consider so-called Herrmann and Hydrostatic mixed formulations of classical linear elasticity and analyse the error associated with locally stabilised finite element a…
Arnold-Winther mixed finite elements for Stokes eigenvalue problems
Joscha Gedicke, Arbaz Khan
This paper is devoted to study the Arnold-Winther mixed finite element method for two dimensional Stokes eigenvalue problems using the stress-velocity formulation. A priori error e…
Robust a posteriori error estimators for mixed approximation of nearly incompressible elasticity
Arbaz Khan, Catherine E. Powell, David J. Silvester
This paper is concerned with the analysis and implementation of robust finite element approximation methods for mixed formulations of linear elasticity problems where the elastic s…
Least-squares spectral element preconditioners for fourth order elliptic problems
Akhlaq Husain, Arbaz Khan
The goal of this paper is to propose preconditioners for the system of linear equations that arises from a discretization of fourth order elliptic problems using spectral element m…