Search Results - "Kassem, Mustapha"

FEM for time-fractional diffusion equations, novel optimal error analyses by MUSTAPHA, KASSEM

“…A semidiscrete Galerkin finite element method applied to time-fractional diffusion equations with time-space dependent diffusivity on bounded convex spatial…”
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A Superconvergent discontinuous Galerkin method for Volterra integro-differential equations, smooth and non-smooth kernels by MUSTAPHA, KASSEM

“…-version discontinuous Galerkin (DG) method and derive nodal error bounds that are explicit in the parameters of interest. In the case of non-smooth kernel, it…”
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Discontinuous Galerkin method for an evolution equation with a memory term of positive type by MUSTAPHA, KASSEM, MCLEAN, WILLIAM

“…We consider an initial value problem for a class of evolution equations incorporating a memory term with a weakly singular kernel bounded by C(t-s)^{\alpha…”
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Decay rate of a weakly dissipative viscoelastic plate equation with infinite memory by Anaya, Khaleel, Messaoudi, Salim A., Mustapha, Kassem

“…In this paper, a weakly dissipative viscoelastic plate equation with an infinite memory is considered. We show a general energy decay rate for a wide class of…”
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Analysis of subdiffusion in disordered and fractured media using a Grünwald-Letnikov fractional calculus model by Obembe, Abiola D., Abu-Khamsin, Sidqi A., Hossain, M. Enamul, Mustapha, Kassem

“…The increasing applications of fractional calculus in simulating the anomalous transport behavior in disordered and fractured heterogeneous porous media has…”
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Inverse source in two-parameter anomalous diffusion, numerical algorithms, and simulations over graded time meshes by Furati, Khaled M., Mustapha, Kassem, Sarumi, Ibrahim O., Iyiola, Olaniyi S.

“…We consider an inverse source two-parameter sub-diffusion model subject to a non-local initial condition. The problem models several physical processes, among…”
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Bayesian calibration of order and diffusivity parameters in a fractional diffusion equation by Alzahrani, Hasnaa H, Lucchesi, Marco, Mustapha, Kassem, Le Maître, Olivier P, Knio, Omar M

“…Abstract This work focuses on parameter calibration of a variable-diffusivity fractional diffusion model. A random, spatially-varying diffusivity field with…”
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Time-stepping discontinuous Galerkin methods for fractional diffusion problems by Mustapha, Kassem

“…Time-stepping h p -versions discontinuous Galerkin (DG) methods for the numerical solution of fractional subdiffusion problems of order - α with - 1 < α < 0…”
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Time-stepping error bounds for fractional diffusion problems with non-smooth initial data by McLean, William, Mustapha, Kassem

“…We apply the piecewise constant, discontinuous Galerkin method to discretize a fractional diffusion equation with respect to time. Using Laplace transform…”
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SUPERCONVERGENCE OF A DISCONTINUOUS GALERKIN METHOD FOR FRACTIONAL DIFFUSION AND WAVE EQUATIONS by MUSTAPHA, KASSEM, MCLEAN, WILLIAM

“…We consider an initial-boundary value problem for ${\partial _t}u - \partial _t^{ - \alpha }{\nabla ^2}u = f\left( x \right)$ , that is, for a fractional…”
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A hybridizable discontinuous Galerkin method for fractional diffusion problems by Cockburn, Bernardo, Mustapha, Kassem

“…We study the use of the hybridizable discontinuous Galerkin (HDG) method for numerically solving fractional diffusion equations of order - α with - 1 < α < 0 …”
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Uniform stability for a spatially-discrete, subdiffusive Fokker-Planck equation by McLean, William, Mustapha, Kassem

“…Numerical Algorithms 89:1441-1463 (2022) We prove stability estimates for the spatially discrete, Galerkin solution of a fractional Fokker-Planck equation,…”
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Error profile for discontinuous Galerkin time stepping of parabolic PDEs by McLean, William, Mustapha, Kassem

“…We consider the time discretization of a linear parabolic problem by the discontinuous Galerkin (DG) method using piecewise polynomials of degree at most r − 1…”
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Uniform stability for a spatially discrete, subdiffusive Fokker–Planck equation by McLean, William, Mustapha, Kassem

“…We prove stability estimates for the spatially discrete, Galerkin solution of a fractional Fokker–Planck equation, improving on previous results in several…”
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A Mixed FEM for a Time-Fractional Fokker–Planck Model by Karaa, Samir, Mustapha, Kassem, Ahmed, Naveed

“…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,…”
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An α-Robust and Second-Order Accurate Scheme for a Subdiffusion Equation by Mustapha, Kassem, McLean, William, Dick, Josef

“…We investigate a second-order accurate time-stepping scheme for solving a time-fractional diffusion equation with a Caputo derivative of order  α ∈ ( 0 , 1 ) …”
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An implicit finite-difference time-stepping method for a sub-diffusion equation, with spatial discretization by finite elements by Mustapha, K.

“…The numerical solution for a class of sub-diffusion equations involving a parameter in the range - 1 < alpha < 0 is studied. For the time discretization, we…”
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A second-order accurate numerical method for a fractional wave equation by MCLEAN, William, MUSTAPHA, Kassem

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Finite volume element method for two-dimensional fractional subdiffusion problems by Karaa, Samir, Mustapha, Kassem, Pani, Amiya K.

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Piecewise-linear, discontinuous Galerkin method for a fractional diffusion equation by Mustapha, Kassem, McLean, William

“…We use a piecewise-linear, discontinuous Galerkin method for the time discretization of a fractional diffusion equation involving a parameter in the range − 1…”
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