Rodolfo Araya, Cristóbal Bertoglio, Cristian Cárcamo:
Error analysis of pressure reconstruction from discrete velocities
Magnetic Resonance Imaging allows to measure the three-dimensional velocity field of blood flows. Therefore, several methods have been proposed to reconstruct the pressure field from such measurements using the incompressible Navier-Stokes equations. However, those measurements are obtained at limited spatial resolution given by the voxel dimensions in the image. Therefore, the velocity entering to the right-hand-side corresponds to a piecewise linear interpolation of the exact velocity. In this work we propose a strategy for convergence analysis of state-of-the-art pressure reconstruction methods. We show that many terms of different convergence order appear. However, numerical results show that linear order terms dominate, even when increasing the polynomial degree of the pressure.