During design of integrated optical circuits the light propagation inside the optical devices has to be evaluated by means of Maxwells equations. In this contribution a new simulation method based on the Finite Element Method (FEM) will be presented, while most conventional programs use the FDM. The field distribution is calculated over the cross-section of  a waveguide. The electrical vector field is approximated on a 2D-Finite Element (FE) mesh by a combination of hierarchical edge and nodal elements. The transversal field components are expressed by edge elements whereas the longitudinal field component uses the classical node based Finite Elements. This special combination of shape functions allows a consistent representation of the electrical field at material boundaries. So called spurious modes are totally avoided by this formulation. A robust mesh generator automatically creates an appropriate FE-mesh. A mesh density function is used to control the element size. For an h-adaptive mesh refinement the mesh density function has to be changed according to a local error criteria. A subsequent call to the mesh generator will refine the mesh appropriately. Modelling of a straight waveguide leads to an eigenvalue problem for the field distribution and the propagation constant. For adaptive mesh refinement different possibilities are considered. It would be possible to use the residuum as an error indicator, however, an explicit expression for the related error of the electromagnetic field is not available. A new error estimator will be presented, which has only small numerical costs compared to the eigenvalue solution. Integrated optics is characterised by a very high length-to-width ratio of its components. The Beam Propagation Method (BPM) is a method to approximate the wave propagation in complex structures. The wave equation is solved by a space stepping method by repeatedly solving a system of linear equations. This procedure becomes more efficient by using an error indicator to adaptively change the mesh density in the waveguide cross-section and the step width in the propagation direction. Numerical results will be presented to show the convergence behaviour and the efficiency for FE-element types of different order and for different refinement strategies.