Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Simultaneous quasi-optimal convergence in FEM-BEM coupling   We consider the symmetric FEM-BEM coupling that connects two linear elliptic
second order partial differential equations posed in a bounded domain $\Omega$
and its complement, where the exterior problem is restated by an integral
equation on the coupling boundary $\Gamma=\partial\Omega$. We assume that the
corresponding transmission problem admits a shift theorem for data in
$H^{-1+s}$, $s \in [-1,-1+s_0]$, $s_0 > 1/2$. We analyze the discretization by
piecewise polynomials of degree $k$ for the domain variable and piecewise
polynomials of degree $k-1$ for the flux variable on the coupling boundary.
Given sufficient regularity we show that (up to logarithmic factors) the
optimal convergence $O(h^{k+1/2})$ in the $H^{-1/2}(\Gamma)$-norm is obtained
for the flux variable, while classical arguments by C\'ea-type quasi-optimality
and standard approximation results provide only $O(h^k)$ for the overall error
in the natural product norm on $H^1(\Omega)\times H^{-1/2}(\Gamma)$.

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The categories of this paper are: ao-sci
30
The categories of this paper are: q-alg
14
The categories of this paper are: math-ph
5
The categories of this paper are: gr-qc
33
The categories of this paper are: plasm-ph
9
The categories of this paper are: nlin
15
The categories of this paper are: nucl-ex
4
The categories of this paper are: cond-mat
23
The categories of this paper are: solv-int
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The categories of this paper are: dg-ga
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The categories of this paper are: chao-dyn
32
The categories of this paper are: atom-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: bayes-an
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The categories of this paper are: hep-th
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The categories of this paper are: astro-ph