φ-FEM: an optimally convergent and easily implementable immersed boundary method for particulate flows and Stokes equations

We present an immersed boundary method to simulate the creeping motion of a solid in a fluid thanks to the Stokes equation and a FEM element strategy called φ-FEM using the description of the solid with a level-set function. One of the advantages of our method is the use of standard finite element spaces and classical integration tools. We obtain the optimal convergence of the method theoretically and numerically