Hierarchical high order finite element bases for H(div) spaces based on curved meshes for two-dimensional regions or manifolds

作者：

Highlights：

• Innovative two dimensional Hdiv approximation spaces for curved quadrilateral and triangular elements.

• Hdiv bases properly constructed on the master element and mapped to the geometrical elements by the Piola transformation, followed by a normalization procedure.

• Stable convergence with optimal convergence rates, coinciding for primal and dual variables.

• Study of number of condensed equations as a function of the polynomial order of the shape functions.

摘要

•Innovative two dimensional Hdiv approximation spaces for curved quadrilateral and triangular elements.•Hdiv bases properly constructed on the master element and mapped to the geometrical elements by the Piola transformation, followed by a normalization procedure.•Stable convergence with optimal convergence rates, coinciding for primal and dual variables.•Study of number of condensed equations as a function of the polynomial order of the shape functions.

论文关键词：Mixed finite elements,Approximation spaces,Hdiv spaces,Manifold domain

论文评审过程：Received 12 July 2015, Revised 13 December 2015, Available online 6 February 2016, Version of Record 2 March 2016.

论文官网地址：https://doi.org/10.1016/j.cam.2016.01.053