Anisotropic hp-adaptive discontinuous Galerkin method for the numerical solution of time dependent PDEs

We deal with the numerical solution of time dependent problems with the aid of anisotropic hp-grids. We present an algorithm which generates a sequence of anisotropic triangular grids and the corresponding polynomial approximation degrees in such a way that the interpolation error measured in the discrete L∞(0,T;Lq(Ω))-norm (q∈[1,∞] and Ω⊂R2) is under a given tolerance and the number of degrees of freedom is as small as possible. The efficiency of the algorithm is demonstrated by numerical experiments.