A moving mesh method for pitting corrosion of heterogeneous materials

An adaptive moving mesh or r -refinement method for the numerical approximation of pitting corrosion in heterogeneous materials is designed and applied to the problem of pitting corrosion in metals. The pitting corrosion is described by Laplace's equation with a moving boundary where the moving boundary problem is coupled with the partial differential equations describing the mesh movement. We show that the numerical approach is able to track evolving pit geometry for complicated materials with varying crystallography, corrosion-resistant inclusions, and material voids.