A <i>C</i><sup>0</sup> interior penalty method for <i>m</i>th-Laplace equation
نویسندگان
چکیده
In this paper, we propose a C 0 interior penalty method for m th-Laplace equation on bounded Lipschitz polyhedral domain in ℝ d , where and can be any positive integers. The standard H 1 -conforming piecewise r -th order polynomial space is used to approximate the exact solution u integer greater than or equal . Unlike Gudi Neilan [ IMA J. Numer. Anal. 31 (2011) 1734–1753], avoid computing D of numerical each element high normal derivatives along mesh interfaces. Therefore our easily implemented. After proving discrete -norm by natural energy semi-norm associated with method, manage obtain stability optimal convergence respect -norm. error estimate under low regularity assumption also obtained. Numerical experiments validate theoretical estimate.
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ژورنال
عنوان ژورنال: ESAIM
سال: 2022
ISSN: ['1270-900X']
DOI: https://doi.org/10.1051/m2an/2022074