Metric tensors for the interpolation error and its gradient in Lp norm

A unified strategy to derive metric tensors in two and three spatial dimensions for the interpolation error and its gradient in Lp norm is presented. It generates anisotropic adaptive meshes as quasi-uniform ones in the corresponding metric space, which is defined by a metric tensor being computed based on error estimates in different norms. Numerical results show that the corresponding convergence rates for several typical problems are almost optimal.