Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Non-degenerate Eulerian finite element method for solving PDEs on
  surfaces   The paper studies a method for solving elliptic partial differential
equations posed on hypersurfaces in $\mathbb{R}^N$, $N=2,3$. The method builds
upon the formulation introduced in Bertalmio et al., J. Comput. Phys., 174
(2001), 759--780., where a surface equation is extended to a neighborhood of
the surface. The resulting degenerate PDE is then solved in one dimension
higher, but can be solved on a mesh that is unaligned to the surface. We
introduce another extended formulation, which leads to uniformly elliptic
(non-degenerate) equations in a bulk domain containing the surface. We apply a
finite element method to solve this extended PDE and prove the convergence of
finite element solutions restricted to the surface to the solution of the
original surface problem. Several numerical examples illustrate the properties
of the method.

6
The categories of this paper are: astro-ph
35
The categories of this paper are: mtrl-th
4
The categories of this paper are: cond-mat
23
The categories of this paper are: solv-int
34
The categories of this paper are: chem-ph
14
The categories of this paper are: math-ph
13
The categories of this paper are: quant-ph
17
The categories of this paper are: q-fin
9
The categories of this paper are: nlin
22
The categories of this paper are: chao-dyn
24
The categories of this paper are: dg-ga
0
The categories of this paper are: hep-ph
26
The categories of this paper are: bayes-an
27
The categories of this paper are: comp-gas
7
The categories of this paper are: hep-th
1
The categories of this paper are: cs