2018
DOI: 10.1007/s10543-018-0728-7
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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 C 1 -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's methodThe goal of this paper is to introduce a stabilis… Show more

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Cited by 7 publications
(17 citation statements)
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“…The stabilisation parameter is chosen as α = 10 −5 , and the marking and adaptive refinement strategies are as in [19]. For this problem the contact set is one-dimensional.…”
Section: Numerical Resultsmentioning
confidence: 99%
See 3 more Smart Citations
“…The stabilisation parameter is chosen as α = 10 −5 , and the marking and adaptive refinement strategies are as in [19]. For this problem the contact set is one-dimensional.…”
Section: Numerical Resultsmentioning
confidence: 99%
“…0,E , with V n (u h ) and M nn (u h ) denoting the jumps over interior edges of the Kirchhoff shear force and the normal moment, see [18,19] for more details.…”
Section: Nitsche's Methodsmentioning
confidence: 99%
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“…With regard to unilateral contact of thin structures, a Nitsche approximation of the unilateral contact between a Kirchhoff-Love plate and a rigid obstacle is presented in [24,23]. In these references, the origin of the proposed method is the Kirchhoff-Love plate model subject to a unilateral contact condition.…”
Section: Introduction and Kinematics Of Plate Modelsmentioning
confidence: 99%