Stability and convergence of nonconforming hp finite-element methods

The stability and convergence of nonconforming hp finite-element methods, in particular, the mortar finite-element method and its variants, are established based on a new stability measure for these methods. Using a generalized eigenvalue analysis, estimates for this measure are computed numerically. Our numerical results demonstrate that these nonconforming methods prove to be good candidates for hp, implementation and also behave as well as conforming finite-element methods. The discussion here is primarily in two dimensions, but some extensions to three dimensions are presented as well.