Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Arbitrarily high-order exponential cut-off methods for preserving
  maximum principle of parabolic equations   A new class of high-order maximum principle preserving numerical methods is
proposed for solving parabolic equations, with application to the semilinear
Allen--Cahn equation. The proposed method consists of a $k$th-order multistep
exponential integrator in time, and a lumped mass finite element method in
space with piecewise $r$th-order polynomials and Gauss--Lobatto quadrature. At
every time level, the extra values violating the maximum principle are
eliminated at the finite element nodal points by a cut-off operation. The
remaining values at the nodal points satisfy the maximum principle and are
proved to be convergent with an error bound of $O(\tau^k+h^r)$. The accuracy
can be made arbitrarily high-order by choosing large $k$ and $r$. Extensive
numerical results are provided to illustrate the accuracy of the proposed
method and the effectiveness in capturing the pattern of phase-field problems.

12
The categories of this paper are: nucl-th
7
The categories of this paper are: hep-th
0
The categories of this paper are: hep-ph
25
The categories of this paper are: patt-sol
35
The categories of this paper are: mtrl-th
29
The categories of this paper are: funct-an
36
The categories of this paper are: cmp-lg
11
The categories of this paper are: hep-lat
10
The categories of this paper are: q-bio
30
The categories of this paper are: q-alg
8
The categories of this paper are: hep-ex
19
The categories of this paper are: eess
13
The categories of this paper are: quant-ph
3
The categories of this paper are: physics
9
The categories of this paper are: nlin
23
The categories of this paper are: solv-int