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Professor Kassem Mustapha

Lecturer

PhD in Computational Mathematics, 91色情片, 2004

Science
School of Mathematics & Statistics

I completed my PhD in numerical and computational mathematics at 91色情片 in 2004, under the supervision of Professors M. Ganesh and I. Sloan. Over the years, I have developed a strong research background in applied and computational mathematics.

My current research focuses on developing efficient computational methods for elasticity equations with random parameters. I am also working on various numerical methods for solving both deterministic and stochastic time-fractional diffusion models, including cases with heterogeneous diffusivity. My contributions to this field of research are internationally recognized.
E-mail
k.mustapha@unsw.edu.au
Location
School of Mathematics and Statistics Anita B. Lawrence Centre, 91色情片 Sydney Sydney NSW 2052
  • Journal articles | 2026
    Dick J; Gao H; McLean W; Mustapha K, 2026, 'Time-fractional diffusion equations with randomness, and efficient numerical estimations of expected values', Numerical Algorithms, 101, pp. 1865 - 1883,
    Journal articles | 2026
    Mustapha K; Mclean W; Dick J; Le Gia QT, 2026, 'A simple modification to mitigate locking in conforming FEM for nearly incompressible elasticity', Applied Numerical Mathematics, 221, pp. 18 - 29,
    Journal articles | 2025
    Clarke M; Dick J; Le Gia QT; Mustapha K; Tran T, 2025, 'QUASI-MONTE CARLO SPARSE GRID GALERKIN FINITE ELEMENT METHODS FOR LINEAR ELASTICITY EQUATIONS WITH UNCERTAINTIES', International Journal for Uncertainty Quantification, 15, pp. 77 - 94,
    Journal articles | 2025
    Qiu W; Zheng X; Mustapha K, 2025, 'Numerical approximations for a hyperbolic integrodifferential equation with a non-positive variable-sign kernel and nonlinear-nonlocal damping', Applied Numerical Mathematics, 213, pp. 61 - 76,
    Journal articles | 2024
    Karaa S; Mustapha K; Ahmed N, 2024, 'A Mixed FEM for a Time-Fractional Fokker鈥揚lanck Model', Journal of Scientific Computing, 99,
    Journal articles | 2024
    Mustapha K; McLean W; Dick J, 2024, 'An 伪-Robust and Second-Order Accurate Scheme for a Subdiffusion Equation', Journal of Scientific Computing, 99,
    Journal articles | 2023
    McLean W; Mustapha K, 2023, 'Error profile for discontinuous Galerkin time stepping of parabolic PDEs', Numerical Algorithms, 93, pp. 157 - 177,
    Journal articles | 2023
    Mustapha K; Knio OM; Le Ma卯tre OP, 2023, 'A second-order accurate numerical scheme for a time-fractional Fokker-Planck equation', IMA Journal of Numerical Analysis, 43, pp. 2115 - 2136,
    Journal articles | 2023
    Sarumi IO; Furati KM; Mustapha K; Khaliq AQM, 2023, 'Efficient high-order exponential time differencing methods for nonlinear fractional differential models', Numerical Algorithms, 92, pp. 1261 - 1288,
    Journal articles | 2022
    McLean W; Mustapha K, 2022, 'Uniform stability for a spatially discrete, subdiffusive Fokker鈥揚lanck equation', Numerical Algorithms, 89, pp. 1441 - 1463,
    Journal articles | 2021
    Alzahrani HH; Lucchesi M; Mustapha K; Le Matre OP; Knio OM, 2021, 'Bayesian calibration of order and diffusivity parameters in a fractional diffusion equation', Journal of Physics Communications, 5,
    Journal articles | 2021
    Anaya K; Messaoudi SA; Mustapha K, 2021, 'Decay rate of a weakly dissipative viscoelastic plate equation with infinite memory', Arabian Journal of Mathematics, 10, pp. 31 - 39,
    Journal articles | 2021
    Furati KM; Mustapha K; Sarumi IO; Iyiola OS, 2021, 'Inverse source in two-parameter anomalous diffusion, numerical algorithms, and simulations over graded time meshes', Computational and Applied Mathematics, 40,
    Journal articles | 2021
    McLean W; Mustapha K; Ali R; Knio OM, 2021, 'Erratum to 鈥淩egularity theory for time-fractional advection-diffusion-reaction equations鈥 [Comput. Math. Appl. 79 (2020) 947鈥961] (Computers and Mathematics with Applications (2020) 79(4) (947鈥961), (S0898122119304055), (10.1016/j.camwa.2019.08.008))', Computers and Mathematics with Applications, 85, pp. 82 - 83,
    Journal articles | 2021
    Sarumi IO; Furati KM; Khaliq AQM; Mustapha K, 2021, 'Generalized Exponential Time Differencing Schemes for Stiff Fractional Systems with Nonsmooth Source Term', Journal of Scientific Computing, 86,
    Journal articles | 2020
    Lucchesi M; Allouch S; Le Ma卯tre OP; Mustapha KA; Knio OM, 2020, 'Particle simulation of space鈥揻ractional diffusion equations', Computational Particle Mechanics, 7, pp. 491 - 507,
    Journal articles | 2020
    McLean W; Mustapha K; Ali R; Knio OM, 2020, 'Regularity theory for time-fractional advection鈥揹iffusion鈥搑eaction equations', Computers and Mathematics with Applications, 79, pp. 947 - 961,
    Journal articles | 2020
    Mustapha K, 2020, 'An \bfitl 1 approximation for a fractional reaction-diffusion equation, a second-order error analysis over time-graded meshes', SIAM Journal on Numerical Analysis, 58, pp. 1319 - 1338,
    Journal articles | 2020
    Mustapha KA; Furati KM; Knio OM; Le Ma卯tre OP, 2020, 'A Finite Difference Method for Space Fractional Differential Equations with Variable Diffusivity Coefficient', Communications on Applied Mathematics and Computation, 2, pp. 671 - 688,
    Journal articles | 2019
    Audu JD; Fairag F; Mustapha K, 2019, 'Mixed finite element analysis for generalized Darcy鈥揊orchheimer model in porous media', Journal of Computational and Applied Mathematics, 353, pp. 191 - 203,
    Journal articles | 2019
    McLean W; Mustapha K; Ali R; Knio O, 2019, 'Well-posedness of time-fractional advection-diffusion-reaction equations', Fractional Calculus and Applied Analysis, 22, pp. 918 - 944,
    Journal articles | 2018
    Karaa S; Mustapha K; Pani AK, 2018, 'Optimal Error Analysis of a FEM for Fractional Diffusion Problems by Energy Arguments', Journal of Scientific Computing, 74, pp. 519 - 535,
    Journal articles | 2018
    Le KN; Mclean W; Mustapha K, 2018, 'A semidiscrete finite element approximation of a time-fractional Fokker Planck equation with nonsmooth initial data', SIAM Journal on Scientific Computing, 40, pp. A3831 - A3852,
    Journal articles | 2018
    Mustapha K, 2018, 'Fem for time-fractional diffusion equations, novel optimal error analyses', Mathematics of Computation, 87, pp. 2259 - 2272,
    Journal articles | 2018
    Obembe AD; Abu-Khamsin SA; Hossain ME; Mustapha K, 2018, 'Analysis of subdiffusion in disordered and fractured media using a Gr眉nwald-Letnikov fractional calculus model', Computational Geosciences, 22, pp. 1231 - 1250,
    Journal articles | 2017
    Furati KM; Iyiola OS; Mustapha K, 2017, 'An inverse source problem for a two-parameter anomalous diffusion with local time datum', Computers and Mathematics with Applications, 73, pp. 1008 - 1015,
    Journal articles | 2017
    Karaa S; Mustapha K; Pani AK, 2017, 'Finite volume element method for two-dimensional fractional subdiffusion problems', IMA Journal of Numerical Analysis, 37, pp. 945 - 964,
    Journal articles | 2017
    Obembe AD; Hossain ME; Mustapha K; Abu-Khamsin SA, 2017, 'A modified memory-based mathematical model describing fluid flow in porous media', Computers and Mathematics with Applications, 73, pp. 1385 - 1402,
    Journal articles | 2016
    Le KN; McLean W; Mustapha K, 2016, 'Numerical solution of the time-fractional Fokker-Planck equation with general forcing', SIAM Journal on Numerical Analysis, 54, pp. 1763 - 1784,
    Journal articles | 2016
    Mustapha K; Abdallah B; Furati KM; Nour M, 2016, 'A discontinuous Galerkin method for time fractional diffusion equations with variable coefficients', Numerical Algorithms, 73, pp. 517 - 534,
    Journal articles | 2016
    Mustapha K; Nour M; Cockburn B, 2016, 'Convergence and superconvergence analyses of HDG methods for time fractional diffusion problems', Advances in Computational Mathematics, 42, pp. 377 - 393,
    Journal articles | 2015
    Cockburn B; Mustapha K, 2015, 'A hybridizable discontinuous Galerkin method for fractional diffusion problems', Numerische Mathematik, 130, pp. 293 - 314,
    Journal articles | 2015
    McLean W; Mustapha K, 2015, 'Time-stepping error bounds for fractional diffusion problems with non-smooth initial data', Journal of Computational Physics, 293, pp. 201 - 217,
    Journal articles | 2015
    Mustapha K, 2015, 'Time-stepping discontinuous Galerkin methods for fractional diffusion problems', Numerische Mathematik, 130, pp. 497 - 516,
    Journal articles | 2014
    Mustapha K; Abdallah B; Furati KM, 2014, 'A discontinuous Petrov-Galerkin method for time-fractional diffusion equations', SIAM Journal on Numerical Analysis, 52, pp. 2512 - 2529,
    Journal articles | 2014
    Mustapha K; Sch枚tzau D, 2014, 'Well-posedness of hp -version discontinuous Galerkin methods for fractional diffusion wave equations', IMA Journal of Numerical Analysis, 34, pp. 1426 - 1446,
    Journal articles | 2013
    Mustapha H; Ghorayeb A; Mustapha K, 2013, 'Erratum: Complex flow simulation in natural aquifer (Advanced Engineering Informatics (2009) 23 (288-293))', Advanced Engineering Informatics, 27, pp. 149 - 156,
    Journal articles | 2013
    Mustapha K; Mclean W, 2013, 'Superconvergence of a discontinuous Galerkin method for fractional diffusion and wave equations', SIAM Journal on Numerical Analysis, 51, pp. 491 - 515,
    Journal articles | 2013
    Mustapha K; Ryan JK, 2013, 'Post-processing discontinuous Galerkin solutions to Volterra integro-differential equations: Analysis and simulations', Journal of Computational and Applied Mathematics, 253, pp. 89 - 103,
    Journal articles | 2013
    Mustapha K, 2013, 'A superconvergent discontinuous galerkin method for volterra integro-differential equations, smooth and non-smooth kernels', Mathematics of Computation, 82, pp. 1987 - 2005,
    Journal articles | 2012
    Mustapha H; Ghorayeb A; Mustapha KA, 2012, 'Corrigendum to "Underground flow simulations using parallel finite element method" [Computers & Geosciences 36 (2010) 161-166]', Computers and Geosciences, 49, pp. 267 - 269,
    Journal articles | 2012
    Mustapha K; AlMutawa J, 2012, 'A finite difference method for an anomalous sub-diffusion equation, theory and applications', Numerical Algorithms, 61, pp. 525 - 543,
    Journal articles | 2012
    Mustapha K; Mclean W, 2012, 'Uniform convergence for a discontinuous Galerkin, time-stepping method applied to a fractional diffusion equation', IMA Journal of Numerical Analysis, 32, pp. 906 - 925,
    Journal articles | 2011
    Mclean W; Mustapha K, 2011, 'Piecewise-linear, discontinuous Galerkin method for a fractional diffusion equation', Numerical Algorithms, 56, pp. 159 - 184,
    Journal articles | 2011
    Mustapha K; Brunner H; Mustapha H; Schotzau D, 2011, 'An hp-version discontinuous Galerkin method for integro-differential equations of parabolic type', SIAM Journal on Numerical Analysis, 49, pp. 1369 - 1396,
    Journal articles | 2011
    Mustapha K, 2011, 'An implicit finite-difference time-stepping method for a sub-diffusion equation, with spatial discretization by finite elements', IMA Journal of Numerical Analysis, 31, pp. 719 - 739,
    Journal articles | 2011
    Mustapha K, 2011, 'The hp- and h-versions of the discontinuous and local discontinuous Galerkin methods for one-dimensional singularly perturbed models', Applied Numerical Mathematics, 61, pp. 1223 - 1236,
    Journal articles | 2010
    Mustapha H; Ghorayeb A; Mustapha K; Saramito P, 2010, 'An efficient parallel mixed method for flow simulations in heterogeneous geological media', International Journal of Computer Mathematics, 87, pp. 607 - 618,
    Journal articles | 2010
    Mustapha H; Ghorayeb A; Mustapha KA, 2010, 'Underground flow simulations using parallel finite element method', Computers and Geosciences, 36, pp. 161 - 166,
    Journal articles | 2010
    Mustapha K; Mustapha H, 2010, 'A second-order accurate numerical method for a semilinear integro-differential equation with a weakly singular kernel', IMA Journal of Numerical Analysis, 30, pp. 555 - 578,
    Journal articles | 2009
    Blalecki B; Ganesh M; Mustapha K, 2009, 'An ADI Petrov-galerkin method with quadrature for parabolic problems', Numerical Methods for Partial Differential Equations, 25, pp. 1129 - 1148,
    Journal articles | 2009
    Mustapha K; Mclean W, 2009, 'Convergence analysis of a discontinuous Galerkin method for a sub-diffusion equation', Numerical Algorithms, 52, pp. 69 - 88
    Journal articles | 2009
    Mustapha K, 2009, 'Numerical solution for a sub-diffusion equation with a smooth kernel', Journal of Computational and Applied Mathematics, 231, pp. 735 - 744,
    Journal articles | 2009
    Mustapha KA; Mclean W, 2009, 'Discontinuous galerkin method for an evolution equation with a memory term of positive type', Mathematics of Computation, 78, pp. 1975 - 1995
    Journal articles | 2008
    Mustapha K; Mustapha H, 2008, 'A quadrature finite element method for semilinear second-order hyperbolic problems', Numerical Methods for Partial Differential Equations, 24, pp. 350 - 367,
    Journal articles | 2008
    Mustapha K, 2008, 'A Petrov-Galerkin method for integro-differential equations with a memory term', Anziam Journal, 50, pp. C610 - C624,
    Journal articles | 2007
    Mclean W; Mustapha K, 2007, 'A second-order accurate numerical method for a fractional wave equation', Numerische Mathematik, 105, pp. 481 - 510
    Journal articles | 2007
    Mustapha H; Mustapha K, 2007, 'A new approach to simulating flow in discrete fracture networks with an optimized mesh', SIAM Journal on Scientific Computing, 29, pp. 1439 - 1459,
    Journal articles | 2006
    Bialecki B; Ganesh M; Mustapha KA, 2006, 'A Petrov-Galerkin method with quadrature for semi-linear second-order hyperbolic problems', Numerical Methods for Partial Differential Equations, 22, pp. 1052 - 1069
    Journal articles | 2006
    Ganesh M; Mustapha K, 2006, 'A fully discrete H1-Galerkin method with quadrature for nonlinear advection-diffusion-reaction equations', Numerical Algorithms, 43, pp. 355 - 383,
    Journal articles | 2005
    Bialecki B; Ganesh M; Mustapha KA, 2005, 'A Crank-Nicolson Petrov-Galerkin method with quadrature for semi-linear parabolic problems', Numerical Methods for Partial Differential Equations, 21, pp. 918 - 937
    Journal articles | 2005
    Ganesh M; Mustapha KA, 2005, 'A Crank-Nicolson and ADI Galerkin method with quadrature for hyperbolic problems', Numerical Methods for Partial Differential Equations, 21, pp. 57 - 79
    Journal articles | 2004
    Bialecki B; Ganesh M; Mustapha KA, 2004, 'A Petrov-Galerkin method with quadrature for elliptic boundary value problems', IMA Journal of Numerical Analysis, 24, pp. 157 - 177
    Journal articles | 2004
    Ganesh M; Grigorieff RD; Mustapha KA, 2004, 'Discrete Petrov-Galerkin scheme for boundary value differential andintegral problems: Theory and applications', Mathematical and Computer Modelling, 40, pp. 1323 - 1334
  • Preprints | 2025
    Dick J; Gia QTL; Mustapha K, 2025, Bayesian inference calibration of the modulus of elasticity,
    Preprints | 2025
    Dick J; Ko S; Gia QTL; Mustapha K; Park S, 2025, A decomposition-based robust training of physics-informed neural networks for nearly incompressible linear elasticity,
    Preprints | 2025
    Mustapha K; McLean W; Dick J; Gia QTL, 2025, A simple modification to mitigate locking in conforming FEM for nearly incompressible elasticity,
    Preprints | 2025
    Qiu W; Zheng X; Mustapha K, 2025, Numerical approximations for a hyperbolic integrodifferential equation with a non-positive variable-sign kernel and nonlinear-nonlocal damping,
    Preprints | 2024
    Clarke M; Dick J; Gia QTL; Mustapha K; Tran T, 2024, Quasi-Monte Carlo sparse grid Galerkin finite element methods for linear elasticity equations with uncertainties,
    Preprints | 2024
    Dick J; Gao H; McLean W; Mustapha K, 2024, Time-fractional diffusion equations with randomness, and efficient numerical estimations of expected values,
    Preprints | 2024
    Karaa S; Mustapha K; Ahmed N, 2024, A mixed FEM for a time-fractional Fokker-Planck model,
    Preprints | 2024
    Mustapha K; McLean W; Dick J, 2024, An $伪$-robust and second-order accurate scheme for a subdiffusion equation,
    Preprints | 2022
    McLean W; Mustapha K, 2022, Error Profile for Discontinuous Galerkin Time Stepping of Parabolic PDEs,
    Preprints | 2021
    Mustapha K; Knio OM; Ma卯tre OPL, 2021, A second-order accurate numerical scheme for a time-fractional Fokker-Planck equation,
    Preprints | 2020
    McLean W; Mustapha K, 2020, Uniform stability for a spatially-discrete, subdiffusive Fokker-Planck equation,
    Preprints | 2020
    Mustapha K, 2020, FEM for time-fractional diffusion equations, novel optimal error analyses,
    Preprints | 2019
    Furati KM; Mustapha K; Sarumi IO; Iyiola OS, 2019, Inverse source in two-parameter anomalous diffusion, numerical algorithms and simulations over graded time-meshes,
    Preprints | 2019
    Le KN; McLean W; Mustapha K, 2019, A semidiscrete finite element approximation of a time-fractional Fokker-Planck equation with nonsmooth initial data,
    Preprints | 2019
    McLean W; Mustapha K; Ali R; Knio OM, 2019, Regularity theory for time-fractional advection-diffusion-reaction equations,
    Preprints | 2019
    Mustapha K, 2019, An L1 approximation for a fractional reaction-diffusion equation, a second-order error analysis over time-graded meshes,
    Preprints | 2018
    Karaa S; Mustapha K; Pani AK, 2018, Optimal error analysis of a FEM for fractional diffusion problems by energy arguments,
    Preprints | 2018
    McLean W; Mustapha K; Ali R; Knio O, 2018, Well-posedness of time-fractional, advection-diffusion-reaction equations,
    Preprints | 2018
    Mustapha K; Furati K; Knio OM; Maitre OL, 2018, A finite difference method for space fractional differential equations with variable diffusivity coefficient,
    Preprints | 2017
    Allouch S; Lucchesi M; Ma卯tre OPL; Mustapha KA; Knio OM, 2017, Particle Simulation of Fractional Diffusion Equations,
    Preprints | 2016
    Furati KM; Iyiola OS; Mustapha K, 2016, An inverse source problem for a two-parameter anomalous diffusion with local time datum,
    Preprints | 2015
    Karaa S; Mustapha K; Pani AK, 2015, Finite volume element method for two-dimensional fractional subdiffusion problems,
    Preprints | 2015
    Le KN; McLean W; Mustapha K, 2015, Numerical solution of the time-fractional Fokker-Planck equation with general forcing,
    Preprints | 2015
    Mustapha K; Abdallah B; Furati KM; Nour M, 2015, A discontinuous Galerkin method for time fractional diffusion equations with variable coefficients,
    Preprints | 2014
    Cockburn B; Mustapha K, 2014, A hybridizable discontinuous Galerkin method for fractional diffusion problems,
    Preprints | 2014
    McLean W; Mustapha K, 2014, Time-stepping error bounds for fractional diffusion problems with non-smooth initial data,
    Preprints | 2014
    Mustapha K; Abdallah B; Furati K, 2014, A discontinuous Petrov-Galerkin method for time-fractional diffusion equations,
    Preprints | 2014
    Mustapha K; Nour M; Cockburn B, 2014, Convergence and superconvergence analyses of HDG methods for time fractional diffusion problems,
    Preprints | 2014
    Mustapha K, 2014, Time-stepping discontinuous Galerkin methods for fractional diffusion problems,
    Preprints | 2013
    Mustapha K, 2013, A Superconvergent discontinuous Galerkin method for Volterra integro-differential equations, smooth and non-smooth kernels,
    Preprints | 2012
    Mustapha K; McLean W, 2012, Superconvergence of a discontinuous Galerkin method for fractional diffusion and wave equations,

I successfully applied for several research grants. These are some of them:

1-听2016-2018, KFUPM-KAUST grant (with Khaled Furati). Title: Fractional Diffusion Modeling of Transport in the Environment, budget: 123,576 SAR.

2-听2014-2016, NSTIP grant (with Bernardo Cockburn, Jaafar AlMutawa and Jamal Al-Smail). Title: Efficient numerical methods for simulating fractional diffusion models, budget: 697,600 SAR

3-听2014-2016, ARC discovery grant (with Bruce Henry and William McLean). Title: Advanced mathematical modeling and computation of fractional sub-diffusion problems in complex domains,udget: 345,000 AUD.

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