Hybridization and stabilization for hp-finite element methods

In this paper various hybrid hp-finite element methods are discussed for elliptic model problems. In particular, a stabilized primal-hybrid hp-method is introduced which approximatively ensures continuity conditions across element interfaces and avoids the enrichment of the primal discretization space as usually required to fulfill some discrete inf-sup condition. A priori as well as a posteriori error estimates are derived for this method. The stabilized primal-hybrid hp-method is also applied to a model obstacle problem since it admits the definition of pointwise constraints. The paper also describes some extensions of primal, primal-mixed and dual-mixed methods as well as their hybridizations to hp-finite elements. In numerical experiments the convergence properties of the stabilized primal-hybrid hp-method are discussed and compared to all the other hp-methods introduced in this paper. The applicability of the a posteriori error estimates to drive h- and hp-adaptive schemes is also investigated.