ABSTRACT
The variational multiscale method provides a framework for construction of adaptive multiscale finite element methods. A new adaptive finite element method is presented based on the variational multiscale method and an a posteriori error estimate in the energy norm for this method. The estimate captures crucial parameters of the method and shows how they are related. An adaptive algorithm is presented that tunes these parameters automatically according to the a posteriori error estimate. Finally, it is shown how the method works in practice by presenting a numerical example.