Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Energy conserving SUPG methods for compatible finite element schemes in
  numerical weather prediction   We present an energy conserving space discretisation based on a Poisson
bracket that can be used to derive the dry compressible Euler as well as
thermal shallow water equations. It is formulated using the compatible finite
element method, and extends the incorporation of upwinding for the shallow
water equations as described in Wimmer, Cotter, and Bauer (2019). While the
former is restricted to DG upwinding, an energy conserving SUPG scheme for the
(partially) continuous Galerkin thermal field space is newly introduced here.
The energy conserving property is validated by coupling the Poisson bracket
based spatial discretisation to an energy conserving time discretisation.
Further, the discretisation is demonstrated to lead to an improved temperature
field development with respect to stability when upwinding is included. An
approximately energy conserving full discretisation with a smaller
computational cost is also presented.

9
The categories of this paper are: nlin
23
The categories of this paper are: solv-int
36
The categories of this paper are: cmp-lg
11
The categories of this paper are: hep-lat
5
The categories of this paper are: gr-qc
21
The categories of this paper are: adap-org
14
The categories of this paper are: math-ph
6
The categories of this paper are: astro-ph
20
The categories of this paper are: acc-phys
35
The categories of this paper are: mtrl-th
28
The categories of this paper are: alg-geom
15
The categories of this paper are: nucl-ex
13
The categories of this paper are: quant-ph
7
The categories of this paper are: hep-th
37
The categories of this paper are: supr-con
4
The categories of this paper are: cond-mat