A stabilised finite element method for the plate obstacle problem
arXiv:1711.0416617 citationsh-index: 38
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Provides a new numerical approach for solving plate obstacle problems, which is important for engineering applications involving contact mechanics.
Introduced a stabilised finite element method for the Kirchhoff plate obstacle problem with conforming C1 elements, providing a priori and a posteriori error estimates and demonstrating effectiveness for elastic and rigid obstacles.
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.