Kassem Mustapha

Superconvergence of a Discontinuous Galerkin Method for Fractional Diffusion and Wave Equations

We consider an initial-boundary value problem for

Convergence analysis of a discontinuous Galerkin method for a sub-diffusion equation

\partial_tu-\partial_t^{-\alpha}\nabla^2u=f(t)

A New Approach to Simulating Flow in Discrete Fracture Networks with an Optimized Mesh

, that is, for a fractional diffusion (

A Discontinuous Petrov--Galerkin Method for Time-Fractional Diffusion Equations

-1<\alpha<0

Discontinuous Galerkin method for an evolution equation with a memory term of positive type

) or wave (

Time-stepping error bounds for fractional diffusion problems with non-smooth initial data

0<\alpha<1

An

) equation. A numerical solution is found by applying a piecewise-linear, discontinuous Galerkin (DG) method in time combined with a piecewise-linear, conforming finite element method in space. The time mesh is graded appropriately near

hp

t=0

-Version Discontinuous Galerkin Method for Integro-Differential Equations of Parabolic Type

, but the spatial mesh is quasi-uniform. Previously, we proved that the error, measured in the spatial

Convergence and superconvergence analyses of HDG methods for time fractional diffusion problems

L_2