  In the last years, medical computer simulation has seen a great growth in
several scientific branches, from modelling to numerical methods, going through
computer science. The main goals of this incipient discipline are testing
hypotheses before an intervention, or see what effect could have a drug in the
system before actually taking it, among others. In this work we deduce from the
most basic physical principles a one dimensional model for the simulation of
blood flow in elastic arteries. We will provide some historical background, as
well as a brief state of the art of these models. We will also study from a
calculus point of view the equations of the model obtained, achieving an
original result for the formation of shock waves in compliant vessels.
Afterwards we will make some numerical simulations using Galerkin Discontinuous
Finite Element Method. Since this is actually a family of methods, we will
motivate and detail the elections and the implementation strategies.
