Anisotropic $hp$-adaptive method based on interpolation error estimates in the $H^1$-seminorm

[摘要] We develop a new technique which, for the given smooth function, generates the anisotropic triangular grid and the corresponding polynomial approximation degrees based on the minimization of the interpolation error in the broken $H^1$-seminorm. This technique can be employed for the numerical solution of boundary value problems with the aid of finite element methods. We present the theoretical background of this approach and show several numerical examples demonstrating the efficiency of the proposed anisotropic adaptive strategy in comparison with other adaptive approaches.

[学科分类] 应用数学

[关键词] $hp$-methods;anisotropic mesh adaptation;interpolation error estimates