Anisotropic hp-adaptive method based on interpolation error estimates in the -norm

We present a new anisotropic hp-adaptive technique, which can be employed for the numerical solution of various scientific and engineering problems governed by partial differential equations in 2D with the aid of a discontinuous piecewise polynomial approximation. This method generates anisotropic triangular grids and the corresponding polynomial approximation degrees based on the minimization of the interpolation error in the L q -norm ( q ∈ [ 1 , ∞ ] ). We develop the theoretical background of this approach and present several numerical examples demonstrating the efficiency of the anisotropic adaptive strategy.