Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A $C^{0}$ interior penalty method for $m$th-Laplace equation   In this paper, we propose a $C^{0}$ interior penalty method for $m$th-Laplace
equation on bounded Lipschitz polyhedral domain in $\mathbb{R}^{d}$, where $m$
and $d$ can be any positive integers. The standard $H^{1}$-conforming piecewise
$r$-th order polynomial space is used to approximate the exact solution $u$,
where $r$ can be any integer greater than or equal to $m$. Unlike the interior
penalty method in [T.~Gudi and M.~Neilan, {\em An interior penalty method for a
sixth-order elliptic equation}, IMA J. Numer. Anal., \textbf{31(4)} (2011), pp.
1734--1753], we avoid computing $D^{m}$ of numerical solution on each element
and high order normal derivatives of numerical solution along mesh interfaces.
Therefore our method can be easily implemented. After proving discrete
$H^{m}$-norm bounded by the natural energy semi-norm associated with our
method, we manage to obtain stability and optimal convergence with respect to
discrete $H^{m}$-norm. Numerical experiments validate our theoretical estimate.

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The categories of this paper are: cmp-lg
31
The categories of this paper are: ao-sci
16
The categories of this paper are: stat
9
The categories of this paper are: nlin
26
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: dg-ga
22
The categories of this paper are: chao-dyn
18
The categories of this paper are: econ
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The categories of this paper are: supr-con
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The categories of this paper are: mtrl-th
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The categories of this paper are: q-fin
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The categories of this paper are: eess
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The categories of this paper are: chem-ph
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The categories of this paper are: math-ph
3
The categories of this paper are: physics