Published

H(div)-conforming Finite Element Tensors with Constraints

Long Chen and Xuehai Huang

Results in Applied Mathematics, 2024

arXiv   Bibtex coming soon

ABSTRACT:

 A unified construction of $H(\div)$-conforming finite
element tensors, including vector element, symmetric matrix element,
traceless matrix element, and, in general, tensors with linear
constraints, is developed in this work. It is based on the geometric
decomposition of Lagrange elements into bubble functions on each
sub-simplex. Each tensor at a sub-simplex is decomposed into
tangential and normal components. The tangential component forms the
bubble function space, while the normal component characterizes the
trace. Some degrees of freedom can be redistributed to
$(n-1)$-dimensional faces. The developed finite element spaces are
$H(\div)$-conforming and satisfy the discrete inf-sup
condition. Intrinsic bases of the constraint tensor space are also
established.