Fictitious domains and level sets for moving boundary problems. Applications to the numerical simulation of tumor growth

In this work we present a new strategy for solving numerically a (relatively simple) model of tumor growth. In principle, this is devoted to describe avascular growth although, by choosing the parameters appropriately, it also permits to give an idea of the behavior after vascularization. The numerical methods rely on fictitious domain and level set techniques, with a combination of quadratic finite elements and finite differences approximations. We present a collection of numerical results that essentially coincide with others, previously obtained with other techniques.