In this work we develop a novel fully discrete version of the plates complex, an exact Hilbert complex relevant for the mixed formulation of fourth-order problems. The derivation of the discrete complex follows the discrete de Rham paradigm, leading to an arbitrary-order construction that applies to meshes composed of general polygonal elements. The discrete plates complex is then used to derive a novel numerical scheme for Kirchhoff--Love plates, for which a full stability and convergence analysis are performed. Extensive numerical tests complete the exposition.
翻译:在这项工作中,我们开发了一个全新的完全离散的板块综合体,一个与四级问题混合配方相关的精确的希尔伯特综合体。离散综合体的衍生遵循离散的德兰姆模式,导致一个任意的顺序构造,适用于由一般多边形元素构成的模件。离散的板块综合体随后被用来为Kirchhoff-love板块产生一个新的数字图案,为此进行了完全稳定和趋同的分析。广泛的数字测试完成了解析。