Spectral element methods are weighted residual techniques for the numerical solution of partial differential equations, that combine the generality of h-type finite element methods with the accuracy of p-type spectral methods. In light of the dual qualities of the method, adaptive techniques for this method consist of a combination of h- and p- refinement procedures. This thesis presents two key ingredients to the development of adaptive spectral element techniques.

First, a new nonconforming discretization is presented. The new "mortar element method" greatly improves the flexibility of the spectral element approach as regards automatic mesh generation and non-propagating local mesh refinement. The method is based on the introduction of an auxiliary "mortar" trace space and constitutes a new domain decomposition approach, characterized by a clean decoupling of the local internal residual evaluations and the transmission of continuity and boundary conditions. Second, single mesh a posteriori error estimators are developed to estimate the actual error incurred by the discretization on a local per element basis and predict the convergence behaviour of the numerical solution. As a result the error estimators serve as criteria in the decision between h- and p- refinement. The flexibility, accuracy and effectiveness of both developments are illustrated by several examples of incompressible Navier-Stokes calculations.