168 citations · 435 across the 24 of their papers we have counts for
26 papers
Numerical approximations for a hyperbolic integrodifferential equation with a non-positive variable-sign kernel and nonlinear-nonlocal damping
Wenlin Qiu, Xiangcheng Zheng, Kassem Mustapha
This work considers the Galerkin approximation and analysis for a hyperbolic integrodifferential equation, where the non-positive variable-sign kernel and nonlinear-nonlocal dampin…
An -robust and second-order accurate scheme for a subdiffusion equation
Kassem Mustapha, William McLean, Josef Dick
We investigate a second-order accurate time-stepping scheme for solving a time-fractional diffusion equation with a Caputo derivative of order~. The basic idea of our s…
A mixed FEM for a time-fractional Fokker-Planck model
Samir Karaa, Kassem Mustapha, Naveed Ahmed
We propose and analyze a mixed finite element method for the spatial approximation of a time-fractional Fokker--Planck equation in a convex polyhedral domain, where the given drivi…
Error Profile for Discontinuous Galerkin Time Stepping of Parabolic PDEs
William McLean, Kassem Mustapha
We consider the time discretization of a linear parabolic problem by the discontinuous Galerkin (DG) method using piecewise polynomials of degree at most in , for …
A second-order accurate numerical scheme for a time-fractional Fokker-Planck equation
Kassem Mustapha, Omar M. Knio, Olivier P. Le Maître
A time-stepping scheme for solving a time fractional Fokker-Planck equation of order , with a general driving force, is investigated. A stability bound for the se…
Uniform stability for a spatially-discrete, subdiffusive Fokker-Planck equation
William McLean, Kassem Mustapha
We prove stability estimates for the spatially discrete, Galerkin solution of a fractional Fokker-Planck equation, improving on previous results in several respects. Our main goal…
Inverse source in two-parameter anomalous diffusion, numerical algorithms and simulations over graded time-meshes
Khaled M. Furati, Kassem Mustapha, Ibrahim O. Sarumi +1
We consider an inverse source two-parameter sub-diffusion model subject to a nonlocal initial condition. The problem models several physical processes, among them are the microwave…
An L1 approximation for a fractional reaction-diffusion equation, a second-order error analysis over time-graded meshes
Kassem Mustapha
A time-stepping L1 scheme for subdiffusion equation with a Riemann--Liouville time-fractional derivative is developed and analyzed. This is the first paper to show that the L1 sche…
A semidiscrete finite element approximation of a time-fractional Fokker-Planck equation with nonsmooth initial data
Kim Ngan Le, William McLean, Kassem Mustapha
We present a new stability and convergence analysis for the spatial discretization of a time-fractional Fokker--Planck equation in a convex polyhedral domain, using continuous, pie…
Regularity theory for time-fractional advection-diffusion-reaction equations
William McLean, Kassem Mustapha, Raed Ali +1
We investigate the behavior of the time derivatives of the solution to a linear time-fractional, advection-diffusion-reaction equation, allowing space- and time-dependent coefficie…
Well-posedness of time-fractional, advection-diffusion-reaction equations
William McLean, Kassem Mustapha, Raed Ali +1
We establish the well-posedness of an initial-boundary value problem for a general class of time-fractional, advection-diffusion-reaction equations, allowing space- and time-depend…
Particle Simulation of Fractional Diffusion Equations
S. Allouch, M. Lucchesi, O. P. Le Maître +2
This work explores different particle-based approaches to the simulation of one-dimensional fractional subdiffusion equations in unbounded domains. We rely on smooth particle appro…
A finite difference method for space fractional differential equations with variable diffusivity coefficient
K. Mustapha, K. Furati, O. M. Knio +1
Anomalous diffusion is a phenomenon that cannot be modeled accurately by second-order diffusion equations, but is better described by fractional diffusion models. The nonlocal natu…
FEM for time-fractional diffusion equations, novel optimal error analyses
Kassem Mustapha
A semidiscrete Galerkin finite element method applied to time-fractional diffusion equations with time-space dependent diffusivity on bounded convex spatial domains will be studied…
Optimal error analysis of a FEM for fractional diffusion problems by energy arguments
Samir Karaa, Kassem Mustapha, Amiya K. Pani
In this article, the piecewise-linear finite element method (FEM) is applied to approximate the solution of time-fractional diffusion equations on bounded convex domains. Standard…
An inverse source problem for a two-parameter anomalous diffusion with local time datum
Khaled M. Furati, Olaniyi S. Iyiola, Kassem Mustapha
We determine the space-dependent source term for a two-parameter fractional diffusion problem subject to nonlocal non-self-adjoint boundary conditions and two local time-distinct d…
A discontinuous Galerkin method for time fractional diffusion equations with variable coefficients
K. Mustapha, B. Abdallah, K. M. Furati +1
We propose a piecewise-linear, time-stepping discontinuous Galerkin method to solve numerically a time fractional diffusion equation involving Caputo derivative of order $μ\in (0,1…
Finite volume element method for two-dimensional fractional subdiffusion problems
Samir Karaa, Kassem Mustapha, Amiya K. Pani
In this paper, a semi-discrete spatial finite volume (FV) method is proposed and analyzed for approximating solutions of anomalous subdiffusion equations involving a temporal fract…
Numerical solution of the time-fractional Fokker-Planck equation with general forcing
Kim Ngan Le, William McLean, Kassem Mustapha
We study two schemes for a time-fractional Fokker-Planck equation with space- and time-dependent forcing in one space dimension. The first scheme is continuous in time and is discr…
Convergence and superconvergence analyses of HDG methods for time fractional diffusion problems
Kassem Mustapha, Maher Nour, Bernardo Cockburn
We study the hybridizable discontinuous Galerkin (HDG) method for the spatial discretization of time fractional diffusion models with Caputo derivative of order . For each t…
A hybridizable discontinuous Galerkin method for fractional diffusion problems
Bernardo Cockburn, Kassem Mustapha
We study the use of the hybridizable discontinuous Galerkin (HDG) method for numerically solving fractional diffusion equations of order with . For exact time-marching…
Time-stepping discontinuous Galerkin methods for fractional diffusion problems
Kassem Mustapha
Time-stepping -versions discontinuous Galerkin (DG) methods for the numerical solution of fractional subdiffusion problems of order with will be proposed and anal…
A discontinuous Petrov-Galerkin method for time-fractional diffusion equations
Kassem Mustapha, Basheer Abdallah, Khaled Furati
We propose and analyze a time-stepping discontinuous Petrov-Galerkin method combined with the continuous conforming finite element method in space for the numerical solution of tim…
Time-stepping error bounds for fractional diffusion problems with non-smooth initial data
William McLean, Kassem Mustapha
We apply the piecewise constant, discontinuous Galerkin method to discretize a fractional diffusion equation with respect to time. Using Laplace transform techniques, we show that…