An adaptive finite element method for the inequality-constrained Reynolds equation

Tom Gustafsson; Kumbakonam R. Rajagopal; Rolf Stenberg; Juha Videman

doi:10.1016/j.cma.2018.03.004

An adaptive finite element method for the inequality-constrained Reynolds equation

Tom Gustafsson, Kumbakonam R. Rajagopal, Rolf Stenberg^*, Juha Videman

^*Corresponding author for this work

Department of Mathematics and Systems Analysis

Research output: Contribution to journal › Article › Scientific › peer-review

10 Citations (Scopus)

Abstract

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.

Original language	English
Pages (from-to)	156-170
Number of pages	15
Journal	Computer Methods in Applied Mechanics and Engineering
Volume	336
DOIs	https://doi.org/10.1016/j.cma.2018.03.004
Publication status	Published - 1 Jul 2018
MoE publication type	A1 Journal article-refereed

Keywords

Reynolds equation
Stabilized finite element method
Variational inequality

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10.1016/j.cma.2018.03.004

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abstract = "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.",

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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

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SP - 156

EP - 170

JO - Computer Methods in Applied Mechanics and Engineering

JF - Computer Methods in Applied Mechanics and Engineering

ER -

An adaptive finite element method for the inequality-constrained Reynolds equation

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Keywords

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