We present an extended framework for hybrid finite element approximations of self-adjoint, positive definite operators. It covers the cases of primal, mixed, and ultraweak formulations, both at the continuous and discrete levels, and gives rise to conforming discretizations. Our framework allows for flexible continuity restrictions across elements, and includes the extreme cases of conforming and discontinuous hybrid methods. We illustrate an application of the framework to the Kirchhoff-Love plate pending model and present three primal hybrid and two mixed hybrid methods, four of them with numerical examples. In particular, we present conforming frameworks for (in classical meaning) non-conforming elements of Morley, Zienkiewicz triangular, and Hellan-Herrmann-Johnson types.

翻译：本文提出了一种用于自伴正定算子杂交有限元逼近的扩展框架。该框架涵盖了原始、混合及超弱形式化方法，在连续与离散层面均适用，并能产生协调离散化方案。我们的框架允许跨单元采用灵活的连续性约束，包含协调杂交方法与间断杂交方法这两种极端情况。我们展示了该框架在Kirchhoff-Love板弯曲模型中的应用，提出了三种原始杂交方法和两种混合杂交方法，其中四种方法附有数值算例。特别地，我们为Morley型、Zienkiewicz三角型及Hellan-Herrmann-Johnson型（传统意义上的）非协调元建立了协调框架。