An efficient space-time adaptive wavelet Galerkin method for   time-periodic parabolic partial differential equations
  We introduce a multitree-based adaptive wavelet Galerkin algorithm {for} space-time discretized linear parabolic partial differential equations, focusing on time-periodic problems. It is shown that the method converges with the best possible rate in linear complexity and can be applied for a wide range of wavelet bases. We discuss the implementational challenges arising from the Petrov-Galerkin nature of the variational formulation and present numerical results for the heat and a convection-diffusion-reaction equation. 
Sebastian Kestler and Kristina Steih and Karsten Urban
math.NA