  Reduction of computational cost of solutions is a key issue to crack
identification or crack propagation problems. One of the solution is to avoid
re-meshing the domain when the crack position changes or when the crack
extends. To avoid re-meshing, we propose a new finite element approach for the
numerical simulation of discontinuities of displacements generated by cracks
inside elastic media. The approach is based on a fictitious domain method
originally developed for Dirichlet conditions for the Poisson problem and for
the Stokes problem, which is adapted to the Neumann boundary conditions of
crack problems. The crack is represented by level-set functions. Numerical
tests are made with a mixed formulation to emphasize the accuracy of the
method, as well as its robustness with respect to the geometry enforced by a
stabilization technique. In particular an inf-sup condition is theoretically
proven for the latter. A realistic simulation with a uniformly pressurized
fracture inside a volcano is given for illustrating the applicability of the
method.
