Abstract:Adaptive finite element methods are popular in computational science and engineering because of their ability to automatically produce efficient solutions to partial differential equations. While their practical properties have long been understood, a satisfying theory explaining their convergence properties has only been developed in the past decade. Most such convergence results concern methods for controlling the (global) energy norm of the error, which is easiest to work with theoretically but not always the most relevant in practice. In this talk I will present convergence and optimality results for an AFEM for controlling errors in the L2 norm. This is joint work with Rob Stevenson of Amsterdam.