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

A Continuous $hp-$Mesh Model for Discontinuous Petrov-Galerkin Finite Element Schemes with Optimal Test Functions