Two parallel, non-iterative, multi-physics, domain decomposition methods are proposed to solve a coupled time-dependent Stokes-Darcy system with the Beavers-Joseph-Saffman-Jones interface condition. For both methods, spatial discretization is effected using finite element methods. The backward Euler method and a three-step backward differentiation method are used for the temporal discretization. Results obtained at previous time steps are used to approximate the coupling information on the interface between the Darcy and Stokes subdomains at the current time step. Hence, at each time step, only a single Stokes and a single Darcy problem need be solved; as these are uncoupled, they can be solved in parallel. The unconditional stability and convergence of the first method is proved and also illustrated through numerical experiments. The improved temporal convergence and unconditional stability of the second method is also illustrated through numerical experiments.

In this paper we study the dynamics of a vector-transmitted disease using two deterministic models. First, we look at time dependent prevention and treatment efforts, where optimal control theory is applied. Using analytical and numerical techniques, it is shown that there are cost effective control efforts for treatment of hosts and prevention of host-vector contacts. Then, we considered the autonomous counter part of the mode and we established global stability results based on the reproductive number. The model is applied to study the effects of prevention and treatment controls on a malaria disease while keeping the implementation cost at a minimum. Numerical results indicate the effects of the two controls (prevention and treatment) in lowering exposed and infected members of each of the populations. The study also highlights the effects of some model parameters on the results.

The equations of quasi-static poroelasticity which model flow through elastic porous media are considered. It is assumed that the hydraulic conductivity depends nonlinearly on the displacement (the dilatation) of the medium. The existence of a weak solution is proved using the modified Rothe's method. Numerical approximations of solutions by the finite element method are considered. Error estimates are obtained and numerical experiments are conducted to illustrate the theoretical results, and the efficiency and accuracy of the numerical method.