Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Gravitational Self-force Errors of Poisson Solvers on Adaptively Refined
  Meshes   An error in the gravitational force that the source of gravity induces on
itself (a self-force error) violates both the conservation of linear momentum
and the conservation of energy. If such errors are present in a
self-gravitating system and are not sufficiently random to average out, the
obtained numerical solution will become progressively more unphysical with
time: the system will acquire or lose momentum and energy due to numerical
effects. In this paper, we demonstrate how self-force errors can arise in the
case where self-gravity is solved on an adaptively refined mesh when the
refinement is nonuniform. We provide the analytical expression for the
self-force error and numerical examples that demonstrate such self-force errors
in idealized settings. We also show how these errors can be corrected to an
arbitrary order by straightforward addition of correction terms at the
refinement boundaries.

9
The categories of this paper are: nlin
24
The categories of this paper are: dg-ga
32
The categories of this paper are: atom-ph
12
The categories of this paper are: nucl-th
4
The categories of this paper are: cond-mat
21
The categories of this paper are: adap-org
36
The categories of this paper are: cmp-lg
7
The categories of this paper are: hep-th
23
The categories of this paper are: solv-int
34
The categories of this paper are: chem-ph
5
The categories of this paper are: gr-qc
25
The categories of this paper are: patt-sol
26
The categories of this paper are: bayes-an
1
The categories of this paper are: cs
15
The categories of this paper are: nucl-ex
17
The categories of this paper are: q-fin