Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: High-Order Extended Finite Element Methods for Solving Interface
  Problems   In this paper, we study arbitrary order extended finite element (XFE) methods
based on two discontinuous Galerkin (DG) schemes in order to solve elliptic
interface problems in two and three dimensions. Optimal error estimates in the
piecewise $H^1$-norm and in the $L^2$-norm are rigorously proved for both
schemes. In particular, we have devised a new parameter-friendly DG-XFEM
method, which means that no "sufficiently large" parameters are needed to
ensure the optimal convergence of the scheme. To prove the stability of
bilinear forms, we derive non-standard trace and inverse inequalities for
high-order polynomials on curved sub-elements divided by the interface. All the
estimates are independent of the location of the interface relative to the
meshes. Numerical examples are given to support the theoretical results.

21
The categories of this paper are: adap-org
8
The categories of this paper are: hep-ex
13
The categories of this paper are: quant-ph
36
The categories of this paper are: cmp-lg
17
The categories of this paper are: q-fin
29
The categories of this paper are: funct-an
0
The categories of this paper are: hep-ph
32
The categories of this paper are: atom-ph
15
The categories of this paper are: nucl-ex
27
The categories of this paper are: comp-gas
28
The categories of this paper are: alg-geom
25
The categories of this paper are: patt-sol
23
The categories of this paper are: solv-int
37
The categories of this paper are: supr-con
33
The categories of this paper are: plasm-ph
20
The categories of this paper are: acc-phys