Adaptive Multilevel Iterative Techniques for Nonconforming Finite Element Discretizations

| We consider adaptive multilevel methods for the nonconforming P1 nite element approximation of linear second order elliptic boundary value problems. Emphasis is on the eecient solution of the discretized problems by multilevel preconditioned conjugate gradient iterations with respect to an adaptively generated hierarchy of possibly highly nonuniform triangulations. Local reenement of the elements of the triangulations is done by means of an eecient and reliable element-oriented a posteriori error estimator that can be derived by a defect correction in a higher order ansatz space and its hierarchical two-level splitting. The performance of the preconditioners and the error estimator is illustrated by some test examples. Further, numerical results are given for the reverse biased pn-junction in semiconductor device simulation and the two-group diiusion equations modeling the neutron uxes in nuclear reactors.