  In our work we focus on the accurate computation of light propagation in
finite size photonic crystal structures with the finite element method (FEM).
We discuss how we utilize numerical concepts like high-order finite elements,
transparent boundary conditions and goal-oriented error estimators for adaptive
grid refinement in order to compute radiation leakage in photonic crystal
fibers and waveguides. Due to the fast convergence of our method we can use it
e.g. to optimize the design of photonic crystal structures with respect to
geometrical parameters, to minimize radiation losses and to compute
attenutation spectra for different geometries.
