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 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.

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