2017/11/28 by Katharina Rafetseder, Rafetseder, Katharina, Walter Zulehner +1
Engineering · #65N22 #65N30 #74K20 #Advanced Numerical Methods in Computational Mathematics #Elasticity and Material Modeling #FOS: Mathematics #Numerical Analysis (math.NA) #Numerical methods in engineering
paper · pdf · doi:10.48550/arxiv.1711.10260
openalex publication_date 2017/11/28 · openalex created_date 2022/10/04 · openalex updated_date 2026/07/28
For Kirchhoff plate bending problems on domains whose boundaries are\ncurvilinear polygons a discretization method based on the consecutive solution\nof three second-order problems is presented. In Rafetseder and Zulehner\n(preprint, arXiv:1703.07962) a new mixed variational formulation of this\nproblem is introduced using a nonstandard Sobolev space (and an associated\nregular decomposition) for the bending moments. In case of a polygonal domain\nthe coupling condition for the two components in the decomposition can be\ninterpreted as standard boundary conditions, which allows for an equivalent\nreformulation as a system of three (consecutively to solve) second-order\nelliptic problems. The extension of this approach to curvilinear polygonal\ndomains poses severe difficulties. Therefore, we propose in this paper an\nalternative approach based on Lagrange multipliers.\n