Mesh independence of semismooth Newton methods

ao. Univ.-Prof. Dipl.-Ing. Dr. Michael Hintermüller

March 31, 2003, 10:15 a.m. T 111

For a class of semismooth operator equations a mesh independence result for generalized Newton methods is established. The main result states that the continuous and the discrete Newton process, when initialized properly, converge q-linearly with the same rate. The problem class considered in the paper includes MCP-function based reformulations of first order conditions of a class of control constrained optimal control problems for partial differential equations for which a numerical validation of the theoretical results is given.