TY - JOUR
T1 - An adaptive finite element method for the inequality-constrained Reynolds equation
AU - Gustafsson, Tom
AU - Rajagopal, Kumbakonam R.
AU - Stenberg, Rolf
AU - Videman, Juha
PY - 2018/7/1
Y1 - 2018/7/1
N2 - We present a stabilized finite element method for the numerical solution of cavitation in lubrication, modeled as an inequality-constrained Reynolds equation. The cavitation model is written as a variable coefficient saddle-point problem and approximated by a residual-based stabilized method. Based on our recent results on the classical obstacle problem, we present optimal a priori estimates and derive novel a posteriori error estimators. The method is implemented as a Nitsche-type finite element technique and shown in numerical computations to be superior to the usually applied penalty methods.
AB - We present a stabilized finite element method for the numerical solution of cavitation in lubrication, modeled as an inequality-constrained Reynolds equation. The cavitation model is written as a variable coefficient saddle-point problem and approximated by a residual-based stabilized method. Based on our recent results on the classical obstacle problem, we present optimal a priori estimates and derive novel a posteriori error estimators. The method is implemented as a Nitsche-type finite element technique and shown in numerical computations to be superior to the usually applied penalty methods.
KW - Reynolds equation
KW - Stabilized finite element method
KW - Variational inequality
UR - http://www.scopus.com/inward/record.url?scp=85044448936&partnerID=8YFLogxK
U2 - 10.1016/j.cma.2018.03.004
DO - 10.1016/j.cma.2018.03.004
M3 - Article
AN - SCOPUS:85044448936
VL - 336
SP - 156
EP - 170
JO - Computer Methods in Applied Mechanics and Engineering
JF - Computer Methods in Applied Mechanics and Engineering
SN - 0045-7825
ER -