Submitted

Geometric Decompositions of H(div)-conforming Finite Element Tensors, Part I: Vector and Matrix Functions

Long Chen and Xuehai Huang

Submitted

arXiv   Bibtex coming soon

ABSTRACT:

 A unified construction of H(div)-conforming finite elements,
including vector element, symmetric matrix element, and traceless
matrix element, is developed in this work. It is based on the
geometric decomposition of Lagrange elements into bubble functions on
each sub-simplex. Then the vector or matrix at each sub-simplex is
decomposed into the tangential and the normal components. The
tangential component forms the polynomial bubble function space and
the normal component characterizes the trace of div operator. Some
degrees of freedom on the normal component can be redistributed
facewisely. Discrete inf-sup conditions are verified.