Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Analysis of the Fourier series Dirichlet-to-Neumann boundary condition
  of the Helmholtz equation and its application to finite element methods   It is well known that the Fourier series Dirichlet-to-Neumann (DtN) boundary
condition can be used to solve the Helmholtz equation in unbounded domains. In
this work, applying such DtN boundary condition and using the finite element
method, we solve and analyze a two dimensional transmission problem describing
elastic waves inside a bounded and closed elastic obstacle and acoustic waves
outside it. We are mainly interested in analyzing the DtN boundary condition of
the Helmholtz equation in order to establish the well-posedness results of the
approximated variational equation, and further derive a priori error estimates
involving effects of both the finite element discretization and the DtN
boundary condition truncation. Finally, some numerical results are presented to
illustrate the accuracy of the numerical scheme.

12
The categories of this paper are: nucl-th
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The categories of this paper are: stat
23
The categories of this paper are: solv-int
18
The categories of this paper are: econ
27
The categories of this paper are: comp-gas
34
The categories of this paper are: chem-ph
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The categories of this paper are: acc-phys
21
The categories of this paper are: adap-org
9
The categories of this paper are: nlin
36
The categories of this paper are: cmp-lg
33
The categories of this paper are: plasm-ph
4
The categories of this paper are: cond-mat
1
The categories of this paper are: cs
24
The categories of this paper are: dg-ga
3
The categories of this paper are: physics
30
The categories of this paper are: q-alg