Metric tensors for the interpolation error and its gradient in L^p norm

2012/01/08 by Yin, Xiaobo, Xie, Hehu
#65N30 #65N50 #FOS: Mathematics #Numerical Analysis (math.NA)

paper · doi:10.48550/arxiv.1201.1632

Abstract

A uniform strategy to derive metric tensors in two spatial dimension for interpolation errors and their gradients in L^p norm is presented. It generates anisotropic adaptive meshes as quasi-uniform ones in corresponding metric space, with the metric tensor being computed based on a posteriori error estimates in different norms. Numerical results show that the corresponding convergence rates are always optimal.

Related

• New metric tensors for anisotropic mesh generation
• General theory of interpolation error estimates on anisotropic meshes
• Interpolation Operators for parabolic Problems
• Anisotropic interpolation error estimates using a new geometric parameter
• Macro-element interpolation on tensor product meshes