Multilevel Methods in Finite Elements

Abstract

This survey consists of five parts. In the first section we describe a model problem and a two-level algorithm in order to motivate the multilevel approach. In Section 2 an abstract multilevel algorithm is described and analyzed under some regularity assumptions. An analysis under less stringent assumptions is given in Section 3. Non-nested spaces and varying forms are treated in Section 4. Finally, we show how the multilevel framework provides computationally efficient realizations of norms on Sobolev scales.