On a hierarchical basis multilevel method with nonconforming P1 elements

We develop a hierarchical basis multilevel method for symmetric second order elliptic boundary value problems in two-dimensional polygonal domains based on nonconforming P1 triangular elements. The main result is that the condition number of the hierarchical discretization is bounded byO(k) wherek is the number of refinement levels. For comparison, Yserentant's result yields the sharp boundO(k 2) for the corresponding hierarchical discretization with conforming linear elements.