TY - JOUR
T1 - Nonconforming FEMs for the $p$-Laplace Problem
AU - Liu , D. J.
AU - Li , A. Q.
AU - Chen , Z. R.
JO - Advances in Applied Mathematics and Mechanics
VL - 6
SP - 1365
EP - 1383
PY - 2018
DA - 2018/09
SN - 10
DO - http://doi.org/10.4208/aamm.OA-2018-0117
UR - https://global-sci.org/intro/article_detail/aamm/12715.html
KW - Adaptive finite element methods, nonconforming, $p$-Laplace problem, dual energy.
AB - <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>