Mixed finite elements for Kirchhoff-Love plate bending

05/15/2023

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by   Thomas Führer, et al.

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We present a mixed finite element method with parallelogram meshes for the Kirchhoff-Love plate bending model. Critical ingredient is the construction of appropriate basis functions that are conforming in terms of a sufficiently large tensor space and allow for any kind of physically relevant Dirichlet and Neumann boundary conditions. For Dirichlet boundary conditions, and polygonal convex or non-convex plates that can be discretized by parallelogram meshes, we prove quasi-optimal convergence of the mixed scheme. Numerical results for regular and singular examples with different boundary conditions illustrate our findings.