TY - JOUR
T1 - A C0 interior penalty method for mth-Laplace equation
AU - Chen, Huangxin
AU - Li, Jingzhi
AU - Qiu, Weifeng
PY - 2022/11
Y1 - 2022/11
N2 - In this paper, we propose a C0 interior penalty method for mth-Laplace equation on bounded Lipschitz polyhedral domain in Double-struck capital ℝd, where m and d can be any positive integers. The standard H1-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 Gudi and Neilan [IMA J. Numer. Anal. 31 (2011) 1734-1753], we avoid computing Dm 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 Hm -norm bounded by the natural energy semi-norm associated with our method, we manage to obtain stability and optimal convergence with respect to discrete Hm -norm. The error estimate under the low regularity assumption of the exact solution is also obtained. Numerical experiments validate our theoretical estimate.
AB - In this paper, we propose a C0 interior penalty method for mth-Laplace equation on bounded Lipschitz polyhedral domain in Double-struck capital ℝd, where m and d can be any positive integers. The standard H1-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 Gudi and Neilan [IMA J. Numer. Anal. 31 (2011) 1734-1753], we avoid computing Dm 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 Hm -norm bounded by the natural energy semi-norm associated with our method, we manage to obtain stability and optimal convergence with respect to discrete Hm -norm. The error estimate under the low regularity assumption of the exact solution is also obtained. Numerical experiments validate our theoretical estimate.
KW - C-0 interior penalty
KW - mth-Laplace equation
KW - stabilization
KW - error estimates
KW - FINITE-DIFFERENCE SCHEME
KW - ELEMENT SPACES
KW - ENERGY
UR - http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcAuth=LinksAMR&SrcApp=PARTNER_APP&DestLinkType=FullRecord&DestApp=WOS&KeyUT=000878309200001
U2 - 10.1051/m2an/2022074
DO - 10.1051/m2an/2022074
M3 - 21_Publication in refereed journal
VL - 56
SP - 2081
EP - 2103
JO - ESAIM: Mathematical Modelling and Numerical Analysis
JF - ESAIM: Mathematical Modelling and Numerical Analysis
SN - 2822-7840
IS - 6
ER -