Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Finite volume schemes of any order on rectangular meshes   In this paper, we analyze vertex-centered finite volume method (FVM) of any
order for elliptic equations on rectangular meshes. The novelty is a unified
proof of the inf-sup condition, based on which, we show that the FVM
approximation converges to the exact solution with the optimal rate in the
energy norm. Furthermore, we discuss superconvergence property of the FVM
solution. With the help of this superconvergence result, we find that the FVM
solution also converges to the exact solution with the optimal rate in the
$L^2$-norm. Finally, we validate our theory with several numerical experiments.

36
The categories of this paper are: cmp-lg
19
The categories of this paper are: eess
23
The categories of this paper are: solv-int
30
The categories of this paper are: q-alg
0
The categories of this paper are: hep-ph
21
The categories of this paper are: adap-org
8
The categories of this paper are: hep-ex
13
The categories of this paper are: quant-ph
18
The categories of this paper are: econ
12
The categories of this paper are: nucl-th
7
The categories of this paper are: hep-th
24
The categories of this paper are: dg-ga
32
The categories of this paper are: atom-ph
4
The categories of this paper are: cond-mat
15
The categories of this paper are: nucl-ex
5
The categories of this paper are: gr-qc