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Numerical solution of a time-fractional nonlinear Rayleigh-Stokes problem
Mariam Al-Maskari, Samir Karaa
We study a semilinear fractional-in-time Rayleigh-Stokes problem for a generalized second-grade fluid with a Lipschitz continuous nonlinear source term and initial data $u_0\in\dot…
Galerkin Type Methods for Semilinear Time-Fractional Diffusion Problems
Samir Karaa
We derive optimal -error estimates for semilinear time-fractional subdiffusion problems involving Caputo derivatives in time of order , for cases with smooth and n…
Galerkin FEM for a time-fractional Oldroyd-B fluid problem
Mariam Al-Maskari, Samir Karaa
We consider the numerical approximation of a generalized fractional Oldroyd-B fluid problem involving two Riemann-Liouville fractional derivatives in time. We establish regularity…
Semidiscrete Finite Element Analysis of Time Fractional Parabolic Problems: A Unified Approach
Samir Karaa
In this paper, we consider the numerical approximation of time-fractional parabolic problems involving Caputo derivatives in time of order , . We derive optimal error es…
Error analysis of a finite volume element method for fractional order evolution equations with nonsmooth initial data
Samir Karaa, Amiya K. Pani
In this paper, a finite volume element (FVE) method is considered for spatial approximations of time-fractional diffusion equations involving a Riemann-Liouville fractional derivat…
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…
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…
A Priori Error Estimates for Mixed Finite Element -Schemes for the Wave Equation
Samir Karaa
A family of implicit-in-time mixed finite element schemes is presented for the numerical approximation of the acoustic wave equation. The mixed space discretization is based on the…
On an a posteriori error analysis of mixed finite element Galerkin approximations to a second order wave equation
Samir Karaa, Amiya K. Pani
In this article, a posteriori error analysis is developed for mixed finite element Galerkin approximations to a second order linear hyperbolic equation. Based on mixed elliptic rec…
A Priori -estimates for Discontinuous Galerkin Approximations to Linear Hyperbolic Integro-Differential Equations
Samir Karaa, Amiya K. Pani, Sangita Yadav
An -discontinuous Galerkin (DG) method is applied to a class of second order linear hyperbolic integro-differential equations. Based on the analysis of an expanded mixed type R…
A priori error estimates for finite volume element approximations to second order linear hyperbolic integro-differential equations
Samir Karaa, Amiya K. Pani
In this paper, both semidiscrete and completely discrete finite volume element methods (FVEMs) are analyzed for approximating solutions of a class of linear hyperbolic integro- dif…
Optimal error estimates of mixed FEMs for second order hyperbolic integro-differential equations with minimal smoothness on initial data
Samir Karaa, Amiya K. Pani
In this article, mixed finite element methods are discussed for a class of hyperbolic integro-differential equations (HIDEs). Based on a modification of the nonstandard energy form…