  In this article we introduce a procedure, which allows to recover the
potentially very good approximation properties of tensor-based model reduction
procedures for the solution of partial differential equations in the presence
of interfaces or strong gradients in the solution which are skewed with respect
to the coordinate axes. The two key ideas are the location of the interface
either by solving a lower-dimensional partial differential equation or by using
data functions and the subsequent removal of the interface of the solution by
choosing the determined interface as the lifting function of the Dirichlet
boundary conditions. We demonstrate in numerical experiments for linear
elliptic equations and the reduced basis-hierarchical model reduction approach
that the proposed procedure locates the interface well and yields a
significantly improved convergence behavior even in the case when we only
consider an approximation of the interface.
