Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Sparse spectral and p-finite element methods for partial differential
  equations on disk slices and trapeziums   Sparse spectral methods for solving partial differential equations have been
derived in recent years using hierarchies of classical orthogonal polynomials
on intervals, disks, and triangles. In this work we extend this methodology to
a hierarchy of non-classical orthogonal polynomials on disk slices (e.g. a
half-disk) and trapeziums. This builds on the observation that sparsity is
guaranteed due to the boundary being defined by an algebraic curve, and that
the entries of partial differential operators can be determined using formulae
in terms of (non-classical) univariate orthogonal polynomials. We apply the
framework to solving the Poisson, variable coefficient Helmholtz, and
Biharmonic equations.

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The categories of this paper are: stat
7
The categories of this paper are: hep-th
23
The categories of this paper are: solv-int
37
The categories of this paper are: supr-con
8
The categories of this paper are: hep-ex
11
The categories of this paper are: hep-lat
27
The categories of this paper are: comp-gas
32
The categories of this paper are: atom-ph
0
The categories of this paper are: hep-ph
9
The categories of this paper are: nlin
12
The categories of this paper are: nucl-th
36
The categories of this paper are: cmp-lg
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The categories of this paper are: chao-dyn
18
The categories of this paper are: econ
29
The categories of this paper are: funct-an
13
The categories of this paper are: quant-ph