Approximating coupled hyperbolic-parabolic systems arising in enhanced drug delivery

Here, we propose a numerical method that allows us to compute second-order accurate approximations to the solution of the hyperbolic and the parabolic equation. The method can be seen as a fully discrete piecewise linear finite element method or as a finite difference method. The convergence rates for both approximations are unexpected. In fact we prove that the error for the approximation of the pressure and concentration is of second-order with respect to discrete versions of the H1-norm and L2-norm, respectively. Numerical experiments illustrating the theoretical estimates are also presented. A simplified model for ultrasound enhanced drug transport is also discussed.