Adaptive solution of evolution phase change problems with error control

Ricardo Nochetto
Department of Mathematics
University of Maryland

Abstract: We discuss the two main ingredients of adaptivity for parabolic free boundary problems, that is reliable a posteriori error estimation and efficient mesh modification via refinement/coarsening. We show an error representation formula and derive rigorous and computable a posteriori upper bounds, which reveal the effects of degenerate diffusion. We illustrate the performance and potentials of the adaptive method with a number of simulations in 2D and 3D.