A stabilised finite element method for the plate obstacle problem

Tom T. Gustafsson; Rolf Stenberg; Juha Videman

doi:10.1007/s10543-018-0728-7

A stabilised finite element method for the plate obstacle problem

Tom T. Gustafsson
, Rolf Stenberg^*
, Juha Videman

^*Corresponding author for this work

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

10 Citations (Scopus)

Abstract

We introduce a stabilised finite element formulation for the Kirchhoff plate obstacle problem and derive both a priori and residual-based a posteriori error estimates using conforming C1 -continuous finite elements. We implement the method as a Nitsche-type scheme and give numerical evidence for its effectiveness in the case of an elastic and a rigid obstacle.

Original language	English
Pages (from-to)	97-124
Journal	BIT Numerical Mathematics
Volume	59
Issue number	1
DOIs	https://doi.org/10.1007/s10543-018-0728-7
Publication status	Published - 4 Mar 2019
MoE publication type	Not Eligible

Funding

Funding from Tekes (Decision No. 3305/31/2015), the Finnish Cultural Foundation, the Portuguese Science Foundation (FCOMP-01-0124-FEDER-029408) and the Finnish Society of Science and Letters is greatly acknowledged.

Keywords

Obstacle problem
Kirchhoff plate
Stabilised FEM
A posteriori estimate
Nitsche’s method

Access to Document

10.1007/s10543-018-0728-7

https://arxiv.org/abs/1711.04166

Cite this

@article{10c50a81109c422ab872f936ad3c6358,

title = "A stabilised finite element method for the plate obstacle problem",

abstract = "We introduce a stabilised finite element formulation for the Kirchhoff plate obstacle problem and derive both a priori and residual-based a posteriori error estimates using conforming C1 -continuous finite elements. We implement the method as a Nitsche-type scheme and give numerical evidence for its effectiveness in the case of an elastic and a rigid obstacle.",

keywords = "Obstacle problem, Kirchhoff plate, Stabilised FEM, A posteriori estimate, Nitsche{\textquoteright}s method",

author = "Gustafsson, \{Tom T.\} and Rolf Stenberg and Juha Videman",

note = "Publisher Copyright: {\textcopyright} 2018, Springer Nature B.V.",

year = "2019",

month = mar,

day = "4",

doi = "10.1007/s10543-018-0728-7",

language = "English",

volume = "59",

pages = "97--124",

journal = "BIT Numerical Mathematics",

issn = "0006-3835",

publisher = "Springer",

number = "1",

}

TY - JOUR

T1 - A stabilised finite element method for the plate obstacle problem

AU - Gustafsson, Tom T.

AU - Stenberg, Rolf

AU - Videman, Juha

PY - 2019/3/4

Y1 - 2019/3/4

N2 - We introduce a stabilised finite element formulation for the Kirchhoff plate obstacle problem and derive both a priori and residual-based a posteriori error estimates using conforming C1 -continuous finite elements. We implement the method as a Nitsche-type scheme and give numerical evidence for its effectiveness in the case of an elastic and a rigid obstacle.

AB - We introduce a stabilised finite element formulation for the Kirchhoff plate obstacle problem and derive both a priori and residual-based a posteriori error estimates using conforming C1 -continuous finite elements. We implement the method as a Nitsche-type scheme and give numerical evidence for its effectiveness in the case of an elastic and a rigid obstacle.

KW - Obstacle problem

KW - Kirchhoff plate

KW - Stabilised FEM

KW - A posteriori estimate

KW - Nitsche’s method

UR - https://www.scopus.com/pages/publications/85053780246

U2 - 10.1007/s10543-018-0728-7

DO - 10.1007/s10543-018-0728-7

M3 - Article

SN - 0006-3835

VL - 59

SP - 97

EP - 124

JO - BIT Numerical Mathematics

JF - BIT Numerical Mathematics

IS - 1

ER -

A stabilised finite element method for the plate obstacle problem

Abstract

Funding

Keywords

Access to Document

Other files and links

Fingerprint

Cite this