Center for Computational and Stochastic Mathematics

Funder

Organizational Unit

Publications

Numerical analysis of a porous–elastic model for convection enhanced drug delivery

Publication . Ferreira, J. A.; Pinto, L.; Santos, R. F.

Convection enhanced drug delivery (CED) is a technique used to make therapeutic agents reach, through a catheter, sites of difficult access. The name of this technique comes from the convective flow originated by a pressure gradient induced at the tip of the catheter. This flow enhances passive diffusion and allows a more efficient spread of the agents by the target site. CED is particularly useful in the treatment of diseases that affect the central nervous system, where the blood-brain barrier prevents the diffusion of most therapeutic agents from the cerebral blood vessels to the brain interstitial space. In this work we deal with the numerical analysis of a coupled system of partial differential equations that can be used to simulate CED in an elastic medium like brain tissue. The model variables are the fluid velocity, the pressure, the tissue deformation, and the agents concentration. We prove the stability of the coupled problem and from the numerical point of view we propose a fully discrete piecewise linear finite element method (FEM). The convergence analysis shows that the method has second order convergence for the pressure, displacement, and concentration. Numerical experiments illustrating the theoretical convergence rates and the behavior of the system are also given.

2022Journal article

Restricted access

Continuous/discontinuous finite element approximation of a 2d navier-stokes problem arising in fluid confinement

Publication . Borges de Oliveira, Hermenegildo; Lopes, Nuno David

In this work, a stationary 2d Navier-Stokes problem with nonlinear feedback forces field is considered in the stream -function formulation. We use the Continuous/Discontinuous Finite Element Method (CD-FEM), with interior penalty terms, to numerically solve the associated boundary -value problem. For the associated continuous and discrete problems, we prove the existence of weak solutions and establish the conditions for their uniqueness. Consistency, stability and convergence of the method are also shown analytically. To validate the numerical model regarding its applicability and robustness, several test cases are carried out.

2024-06Journal article

Restricted access