In this paper, we design numerical methods for a PDE system arising in corrosion modeling. This system describes the evolution of a dense oxide layer. It is based on a drift–diffusion system and includes moving boundary equations. The choice of the numerical methods is justified by a stability analysis and by the study of their numerical performance.… (More)
We consider the numerical solution of the free boundary Bernoulli problem by employing level set formulations. Using a perturbation technique, we derive a second order method that leads to a fast iteration solver. The iteration procedure is adapted in order to work in the case of topology changes. Various numerical experiments confirm the efficiency of the… (More)
We present a numerical method based on a level set formulation to solve the Bernoulli problem. The formulation uses time as a parameter of boundary evolution. The level set formulation enables to consider non connected domains. Numerical experiments show the efficiency of the method if boundary conditions are handled accurately. In particular, the case of… (More)
In most cases authors are permitted to post their version of the article (e.g. in Word or Tex form) to their personal website or institutional repository. Authors requiring further information regarding Elsevier's archiving and manuscript policies are encouraged to visit: a b s t r a c t In this paper, we design numerical methods for a PDE system arising in… (More)
We present an object oriented finite element library written in C++. We outline the main motivations in developing such a library. Through a simple example program we show a typical use of the library. We describe the main class categories and typical problems to solve using the library.