Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Bulk-surface virtual element method for systems of PDEs in two-space
  dimension   In this paper we consider a coupled bulk-surface PDE in two space dimensions.
The model consists of a PDE in the bulk that is coupled to another PDE on the
surface through general nonlinear boundary conditions. For such a system we
propose a novel method, based on coupling a virtual element method [Beir\~ao da
Veiga et al., 2013] in the bulk domain to a surface finite element method
[Dziuk & Elliott, 2013] on the surface. The proposed method, which we coin the
Bulk-Surface Virtual Element Method (BSVEM) includes, as a special case, the
bulk-surface finite element method (BSFEM) on triangular meshes [Madzvamuse &
Chung, 2016]. The method exhibits second-order convergence in space, provided
the exact solution is $H^{2+1/4}$ in the bulk and $H^2$ on the surface, where
the additional $\frac{1}{4}$ is required only in the simultaneous presence of
surface curvature and non-triangular elements. Two novel techniques introduced
in our analysis are (i) an $L^2$-preserving inverse trace operator for the
analysis of boundary conditions and (ii) the Sobolev extension as a replacement
of the lifting operator [Elliott & Ranner, 2013] for sufficiently smooth exact
solutions. The generality of the polygonal mesh can be exploited to optimize
the computational time of matrix assembly. The method takes an optimised
matrix-vector form that also simplifies the known special case of BSFEM on
triangular meshes [Madzvamuse & Chung, 2016]. Three numerical examples
illustrate our findings.

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The categories of this paper are: eess
36
The categories of this paper are: cmp-lg
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The categories of this paper are: hep-th
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The categories of this paper are: math-ph
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The categories of this paper are: nucl-th
33
The categories of this paper are: plasm-ph
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The categories of this paper are: econ
4
The categories of this paper are: cond-mat
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The categories of this paper are: chao-dyn
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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: physics
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The categories of this paper are: quant-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: mtrl-th
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The categories of this paper are: dg-ga