@Article{AAMM-10-6,
author = {Liu, J., D. and Q., Li, A. and Z., R., Chen},
title = {Nonconforming FEMs for the $p$-Laplace Problem},
journal = {Advances in Applied Mathematics and Mechanics},
year = {2018},
volume = {10},
number = {6},
pages = {1365--1383},
abstract = {<p style="text-align: justify;">The $p$-Laplace problems in topology optimization eventually lead to a degenerate
convex minimization problem $E(v):=
∫_ΩW(∇v)dx − ∫_Ωf vdx$ for $v∈W^{1,p}_0(Ω)$ with unique minimizer $u$ and stress $σ := DW(∇u)$. This paper proposes the discrete
Raviart-Thomas mixed finite element method (dRT-MFEM) and establishes its equivalence
with the Crouzeix-Raviart nonconforming finite element method (CR-NCFEM).
The sharper quasi-norm a priori and a posteriori error estimates of this two methods
are presented. Numerical experiments are provided to verify the analysis.</p>},
issn = {2075-1354},
doi = {https://doi.org/10.4208/aamm.OA-2018-0117},
url = {https://global-sci.com/article/73227/nonconforming-fems-for-the-p-laplace-problem}
}