Abstract
For Kirchhoff plate bending problems on domains whose boundaries are curvilinear polygons a discretization method based on the consecutive solution of three second-order problems is presented.
In Rafetseder and Zulehner (SIAM J Numer Anal 56(3):1961–1986, 2018) a new mixed variational formulation of this problem is introduced using a nonstandard Sobolev space (and an associated regular decomposition) for the bending moments. In case of a polygonal domain the coupling condition for the two components in the decomposition can be interpreted as standard boundary conditions, which allows for an equivalent reformulation as a system of three (consecutively to solve) second-order elliptic problems.
The extension of this approach to curvilinear polygonal domains poses severe difficulties. Therefore, we propose in this paper an alternative approach based on Lagrange multipliers.
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References
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Acknowledgement
The research was supported by the Austrian Science Fund (FWF): S11702-N23.
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Rafetseder, K., Zulehner, W. (2019). On a New Mixed Formulation of Kirchhoff Plates on Curvilinear Polygonal Domains. In: Radu, F., Kumar, K., Berre, I., Nordbotten, J., Pop, I. (eds) Numerical Mathematics and Advanced Applications ENUMATH 2017. ENUMATH 2017. Lecture Notes in Computational Science and Engineering, vol 126. Springer, Cham. https://doi.org/10.1007/978-3-319-96415-7_82
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DOI: https://doi.org/10.1007/978-3-319-96415-7_82
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