  We consider a new fictitious domain approach of higher order accuracy. To
implement Dirichlet conditions we apply the classical Nitsche method combined
with a facet-based stabilization (ghost penalty). Both techniques are combined
with a higher order isoparametric finite element space which is based on a
special mesh transformation. The mesh transformation is build upon a higher
order accurate level set representation and allows to reduce the problem of
numerical integration to problems on domains which are described by piecewise
linear level set functions. The combination of this strategy for the numerical
integration and the stabilized Nitsche formulation results in an accurate and
robust method. We introduce and analyze it and give numerical examples.
