An efficient algorithm for solving a temporal dependence convection model

In this project, a second-order accurate numerical algorithm for solving a time-fractional (non-local) convection model will be investigated. For the time discretization, our numerical method will be based on the popular L1 approximations, combined with the continuous finite elements for the spatial discretizations. Due to the presence of time-dependent driving force (which is practically important) in our model problem, showing the stability and the convergence of the computational scheme are challenging. An appropriate time-graded mesh is required to compensate for the singular behaviour of the continuous solution. Simulations and numerical computations for different classes of time-fractional convection models will be carried out to support our theoretical contributions, and also to illustrate numerically the accuracy of our numerical algorithm.