  We present an anisotropic $hp-$mesh adaptation strategy using a continuous
mesh model for discontinuous Petrov-Galerkin (DPG) finite element schemes with
optimal test functions, extending our previous work on $h-$adaptation. The
proposed strategy utilizes the inbuilt residual-based error estimator of the
DPG discretization to compute both the polynomial distribution and the
anisotropy of the mesh elements. In order to predict the optimal order of
approximation, we solve local problems on element patches, thus making these
computations highly parallelizable. The continuous mesh model is formulated
either with respect to the error in the solution, measured in a suitable norm,
or with respect to certain admissible target functionals. We demonstrate the
performance of the proposed strategy using several numerical examples on
triangular grids.
  Keywords: Discontinuous Petrov-Galerkin, Continuous mesh models, $hp-$
adaptations, Anisotropy
