Numerical analysis of a porous-elastic model for convection enhanced drug delivery (Q2050934)

The authors of this work studied a coupled system of partial differential equations stemming from modeling of the technique of convection-enhanced drug delivery in an elastic medium. The main contribution of the work is the numerical analysis of a piecewise linear finite element method used for the numerical solution of the system. The authors derived energy and stability estimates for the continuous and discrete pressure, displacement, and concentration variables, and conducted a convergence analysis. Second-order convergence for the three discrete quantities in suitable norms was proven. These estimates were verified by a one-dimensional numerical example. Additional one-dimensional numerical examples with varying elastic properties of tissues were presented.