Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: PDE-Based Multidimensional Extrapolation of Scalar Fields over
  Interfaces with Kinks and High Curvatures   We present a PDE-based approach for the multidimensional extrapolation of
smooth scalar quantities across interfaces with kinks and regions of high
curvature. Unlike the commonly used method of [2] in which normal derivatives
are extrapolated, the proposed approach is based on the extrapolation and
weighting of Cartesian derivatives. As a result, second- and third-order
accurate extensions in the $L^\infty$ norm are obtained with linear and
quadratic extrapolations, respectively, even in the presence of sharp geometric
features. The accuracy of the method is demonstrated on a number of examples in
two and three spatial dimensions and compared to the approach of [2]. The
importance of accurate extrapolation near sharp geometric features is
highlighted on an example of solving the diffusion equation on evolving
domains.

36
The categories of this paper are: cmp-lg
37
The categories of this paper are: supr-con
8
The categories of this paper are: hep-ex
27
The categories of this paper are: comp-gas
18
The categories of this paper are: econ
9
The categories of this paper are: nlin
6
The categories of this paper are: astro-ph
33
The categories of this paper are: plasm-ph
12
The categories of this paper are: nucl-th
31
The categories of this paper are: ao-sci
13
The categories of this paper are: quant-ph
29
The categories of this paper are: funct-an
35
The categories of this paper are: mtrl-th
10
The categories of this paper are: q-bio
5
The categories of this paper are: gr-qc
17
The categories of this paper are: q-fin