We present a mixed finite element method with triangular and parallelogram meshes for the Kirchhoff-Love plate bending model. Critical ingredient is the construction of low-dimensional local spaces and appropriate degrees of freedom that provide conformity in terms of a sufficiently large tensor space and that allow for any kind of physically relevant Dirichlet and Neumann boundary conditions. For Dirichlet boundary conditions and polygonal plates, we prove quasi-optimal convergence of the mixed scheme. An a posteriori error estimator is derived for the special case of the biharmonic problem. Numerical results for regular and singular examples illustrate our findings. They confirm expected convergence rates and exemplify the performance of an adaptive algorithm steered by our error estimator.

翻译：本文针对Kirchhoff-Love板弯曲模型，提出了一种适用于三角形和四边形网格的混合有限元方法。关键要素在于构建低维局部空间及恰当的自由度，使其在足够大的张量空间中满足相容性，并能处理所有物理相关的Dirichlet与Neumann边界条件。对于Dirichlet边界条件下的多边形板，我们证明了该混合格式的拟最优收敛性。针对双调和问题的特例，推导了后验误差估计子。正则解与奇异解的数值结果验证了理论发现，不仅确认了预期收敛阶，还展示了由误差估计子引导的自适应算法的性能表现。