By Professor Kassem Ahmad Mustapha

Journal articles

Karaa S; Mustapha K; Ahmed N, 2024, 'A Mixed FEM for a Time-Fractional Fokker–Planck Model', Journal of Scientific Computing, 99, http://dx.doi.org/10.1007/s10915-024-02529-x

Mustapha K; McLean W; Dick J, 2024, 'An α-Robust and Second-Order Accurate Scheme for a Subdiffusion Equation', Journal of Scientific Computing, 99, http://dx.doi.org/10.1007/s10915-024-02554-w

Mustapha K; Knio OM; Le Maître OP, 2023, 'A second-order accurate numerical scheme for a time-fractional Fokker-Planck equation', IMA Journal of Numerical Analysis, 43, pp. 2115 - 2136, http://dx.doi.org/10.1093/imanum/drac031

McLean W; Mustapha K, 2023, 'Error profile for discontinuous Galerkin time stepping of parabolic PDEs', Numerical Algorithms, 93, pp. 157 - 177, http://dx.doi.org/10.1007/s11075-022-01410-y

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, http://dx.doi.org/10.1007/s11075-022-01339-2

McLean W; Mustapha K, 2022, 'Uniform stability for a spatially discrete, subdiffusive Fokker–Planck equation', Numerical Algorithms, 89, pp. 1441 - 1463, http://dx.doi.org/10.1007/s11075-021-01160-3

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, http://dx.doi.org/10.1007/s40065-020-00295-w

McLean W; Mustapha K; Ali R; Knio OM, 2021, 'Erratum to “Regularity theory for time-fractional advection-diffusion-reaction equations” [Comput. Math. Appl. 79 (2020) 947–961] (Computers and Mathematics with Applications (2020) 79(4) (947–961), (S0898122119304055), (10.1016/j.camwa.2019.08.008))', Computers and Mathematics with Applications, 85, pp. 82 - 83, http://dx.doi.org/10.1016/j.camwa.2021.01.008

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, http://dx.doi.org/10.1007/s10915-020-01374-y

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, http://dx.doi.org/10.1007/s40314-020-01399-x

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, http://dx.doi.org/10.1088/2399-6528/AC1507

Mustapha KA; Furati KM; Knio OM; Le Maître 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, http://dx.doi.org/10.1007/s42967-020-00066-6

Lucchesi M; Allouch S; Le Maître OP; Mustapha KA; Knio OM, 2020, 'Particle simulation of space–fractional diffusion equations', Computational Particle Mechanics, 7, pp. 491 - 507, http://dx.doi.org/10.1007/s40571-019-00275-8

McLean W; Mustapha K; Ali R; Knio OM, 2020, 'Regularity theory for time-fractional advection–diffusion–reaction equations', Computers and Mathematics with Applications, 79, pp. 947 - 961, http://dx.doi.org/10.1016/j.camwa.2019.08.008

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, http://dx.doi.org/10.1137/19M1260475

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, http://dx.doi.org/10.1515/fca-2019-0050

Audu JD; Fairag F; Mustapha K, 2019, 'Mixed finite element analysis for generalized Darcy–Forchheimer model in porous media', Journal of Computational and Applied Mathematics, 353, pp. 191 - 203, http://dx.doi.org/10.1016/j.cam.2018.12.009

Obembe AD; Abu-Khamsin SA; Hossain ME; Mustapha K, 2018, 'Analysis of subdiffusion in disordered and fractured media using a Grünwald-Letnikov fractional calculus model', Computational Geosciences, 22, pp. 1231 - 1250, http://dx.doi.org/10.1007/s10596-018-9749-1

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, http://dx.doi.org/10.1137/17M1125261

Mustapha K, 2018, 'Fem for time-fractional diffusion equations, novel optimal error analyses', Mathematics of Computation, 87, pp. 2259 - 2272, http://dx.doi.org/10.1090/mcom/3304

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, http://dx.doi.org/10.1007/s10915-017-0450-7

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, http://dx.doi.org/10.1093/imanum/drw010

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, http://dx.doi.org/10.1016/j.camwa.2016.11.022

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, http://dx.doi.org/10.1016/j.camwa.2016.06.036

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, http://dx.doi.org/10.1007/s11075-016-0106-y

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, http://dx.doi.org/10.1007/s10444-015-9428-x

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, http://dx.doi.org/10.1137/15M1031734

Mustapha K, 2015, 'Time-stepping discontinuous Galerkin methods for fractional diffusion problems', Numerische Mathematik, 130, pp. 497 - 516, http://dx.doi.org/10.1007/s00211-014-0669-2

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, http://dx.doi.org/10.1016/j.jcp.2014.08.050

Cockburn B; Mustapha K, 2015, 'A hybridizable discontinuous Galerkin method for fractional diffusion problems', Numerische Mathematik, 130, pp. 293 - 314, http://dx.doi.org/10.1007/s00211-014-0661-x

Mustapha K; Schötzau D, 2014, 'Well-posedness of hp -version discontinuous Galerkin methods for fractional diffusion wave equations', IMA Journal of Numerical Analysis, 34, pp. 1426 - 1446, http://dx.doi.org/10.1093/imanum/drt048

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, http://dx.doi.org/10.1137/140952107

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, http://dx.doi.org/10.1090/S0025-5718-2013-02689-0

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, http://dx.doi.org/10.1016/j.cam.2013.03.047

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, http://dx.doi.org/10.1016/j.aei.2012.11.002

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, http://dx.doi.org/10.1137/120880719

Mustapha K; AlMutawa J, 2012, 'A finite difference method for an anomalous sub-diffusion equation, theory and applications', Numerical Algorithms, 61, pp. 525 - 543, http://dx.doi.org/10.1007/s11075-012-9547-0

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, http://dx.doi.org/10.1016/j.cageo.2012.03.017

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, http://dx.doi.org/10.1093/imanum/drr027

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, http://dx.doi.org/10.1016/j.apnum.2011.08.001

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, http://dx.doi.org/10.1137/100797114

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, http://dx.doi.org/10.1093/imanum/drp057

Mclean W; Mustapha K, 2011, 'Piecewise-linear, discontinuous Galerkin method for a fractional diffusion equation', Numerical Algorithms, 56, pp. 159 - 184, http://dx.doi.org/10.1007/s11075-010-9379-8

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, http://dx.doi.org/10.1080/00207160802158728

Mustapha H; Ghorayeb A; Mustapha KA, 2010, 'Underground flow simulations using parallel finite element method', Computers and Geosciences, 36, pp. 161 - 166, http://dx.doi.org/10.1016/j.cageo.2008.12.018

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, http://dx.doi.org/10.1093/imanum/drn075

Mustapha K, 2009, 'Numerical solution for a sub-diffusion equation with a smooth kernel', Journal of Computational and Applied Mathematics, 231, pp. 735 - 744, http://dx.doi.org/10.1016/j.cam.2009.04.020

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, http://dx.doi.org/10.1002/num.20391

Mustapha K; Mclean W, 2009, 'Convergence analysis of a discontinuous Galerkin method for a sub-diffusion equation', Numerical Algorithms, 52, pp. 69 - 88

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

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