Metric tensors for the interpolation error and its gradient in norm

A unified strategy to derive metric tensors in two and three spatial dimensions for the interpolation error and its gradient in L p 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.