Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A family of mixed finite elements for the biharmonic equations on
  triangular and tetrahedral grids   This paper introduces a new family of mixed finite elements for solving a
mixed formulation of the biharmonic equations in two and three dimensions. The
symmetric stress $\bm{\sigma}=-\nabla^{2}u$ is sought in the Sobolev space
$H({\rm{div}}\bm{div},\Omega;\mathbb{S})$ simultaneously with the displacement
$u$ in $L^{2}(\Omega)$. Stemming from the structure of
$H(\bm{div},\Omega;\mathbb{S})$ conforming elements for the linear elasticity
problems proposed by J. Hu and S. Zhang, the
$H({\rm{div}}\bm{div},\Omega;\mathbb{S})$ conforming finite element spaces are
constructed by imposing the normal continuity of $\bm{div}\bm{\sigma}$ on the
$H(\bm{div},\Omega;\mathbb{S})$ conforming spaces of $P_{k}$ symmetric tensors.
The inheritance makes the basis functions easy to compute. The discrete spaces
for $u$ are composed of the piecewise $P_{k-2}$ polynomials without requiring
any continuity. Such mixed finite elements are inf-sup stable on both
triangular and tetrahedral grids for $k\geq 3$, and the optimal order of
convergence is achieved. Besides, the superconvergence and the postprocessing
results are displayed. Some numerical experiments are provided to demonstrate
the theoretical analysis.

15
The categories of this paper are: nucl-ex
14
The categories of this paper are: math-ph
11
The categories of this paper are: hep-lat
19
The categories of this paper are: eess
22
The categories of this paper are: chao-dyn
8
The categories of this paper are: hep-ex
4
The categories of this paper are: cond-mat
31
The categories of this paper are: ao-sci
35
The categories of this paper are: mtrl-th
32
The categories of this paper are: atom-ph
9
The categories of this paper are: nlin
16
The categories of this paper are: stat
25
The categories of this paper are: patt-sol
6
The categories of this paper are: astro-ph
24
The categories of this paper are: dg-ga
29
The categories of this paper are: funct-an