Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A new anisotropic finite element method on polyhedral domains:
  interpolation error analysis   Consider the Poisson equation with the Dirichlet boundary condition on a
three-dimensional polyhedral domain. For singular solutions from the
non-smoothness of the domain boundary, we propose new anisotropic tetrahedral
mesh refinement algorithms to improve the convergence of finite element
approximation. The proposed algorithm is simple, explicit, and requires less
geometric conditions on the mesh and on the domain. Then, we develop
interpolation error estimates in suitable weighted spaces for the anisotropic
mesh. These estimates can be used to design optimal finite element methods
approximating singular solutions. We report numerical test results to validate
the method.

18
The categories of this paper are: econ
34
The categories of this paper are: chem-ph
20
The categories of this paper are: acc-phys
12
The categories of this paper are: nucl-th
4
The categories of this paper are: cond-mat
31
The categories of this paper are: ao-sci
11
The categories of this paper are: hep-lat
37
The categories of this paper are: supr-con
14
The categories of this paper are: math-ph
27
The categories of this paper are: comp-gas
10
The categories of this paper are: q-bio
0
The categories of this paper are: hep-ph
23
The categories of this paper are: solv-int
16
The categories of this paper are: stat
13
The categories of this paper are: quant-ph
36
The categories of this paper are: cmp-lg