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.

翻译：本文针对Kirchhoff-Love板弯曲模型，提出一种基于平行四边形网格的混合有限元方法。其关键要素在于构造适当的基函数，这些基函数在足够大的张量空间中具有协调性，并能适用于任意物理相关的Dirichlet和Neumann边界条件。对于Dirichlet边界条件以及可通过平行四边形网格离散的凸多边形或非凸板结构，我们证明了混合格式的拟最优收敛性。针对不同边界条件的正则与奇异示例的数值结果验证了本文的理论发现。