Adaptive mesh refinement and superconvergence for two-dimensional interface problems (Q6486741)

A second-order elliptic interface equation with prescribed jump conditions across an interface and supplied with Dirichlet and/or Neumann boundary conditions is considered. The authors combine the adaptive mesh refinement with an algorithm based on the domain imbedding (Boergers) in order to generate a body fitted mesh. This mesh is intended to resolve the interface with fine geometric details and at the same time to preserve the hierarchical structure. On this structure they construct an efficient algorithm solver and by some superconvergence analysis they provide an estimate in maximum norm. Two numerical experiments are carried out and two spectacular solutions are displayed.