Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A discrete maximum principle for the weak Galerkin finite element method
  on nonuniform rectangular partitions   This article establishes a discrete maximum principle (DMP) for the
approximate solution of convection-diffusion-reaction problems obtained from
the weak Galerkin finite element method on nonuniform rectangular partitions.
The DMP analysis is based on a simplified formulation of the weak Galerkin
involving only the approximating functions defined on the boundary of each
element. The simplified weak Galerkin method has a reduced computational
complexity over the usual weak Galerkin, and indeed provides a discretization
scheme different from the weak Galerkin when the reaction term presents. An
application of the simplified weak Galerkin on uniform rectangular partitions
yields some $5$- and $7$-point finite difference schemes for the second order
elliptic equation. Numerical experiments are presented to verify the discrete
maximum principle and the accuracy of the scheme, particularly the finite
difference scheme.

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The categories of this paper are: quant-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: hep-lat
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The categories of this paper are: bayes-an
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The categories of this paper are: funct-an
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The categories of this paper are: hep-th
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The categories of this paper are: cond-mat
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The categories of this paper are: nucl-th
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The categories of this paper are: patt-sol
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The categories of this paper are: stat
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The categories of this paper are: mtrl-th
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The categories of this paper are: solv-int
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The categories of this paper are: eess
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The categories of this paper are: gr-qc
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The categories of this paper are: ao-sci
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The categories of this paper are: cmp-lg