Mixed finite elements for Kirchhoff–Love plate bending
Thomas Führer and Norbert Heuer
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.