$hp$-anisotropic mesh adaptation technique based on interpolation error estimates

summary:We present a completely new $hp$-anisotropic mesh adaptation technique for the numerical solution of partial differential equations with the aid of a discontinuous piecewise polynomial approximation. This approach generates general anisotropic triangular grids and the corresponding degrees of polynomial approximation based on the minimization of the interpolation error. We develop the theoretical background of this approach and present a numerical example demonstrating the efficiency of this anisotropic strategy in comparison with an isotropic one