In this article we study nonconforming discretizations of Hilbert complexes that involve broken spaces and projection operators to structure-preserving conforming discretizations. Under the usual assumptions for the underlying conforming subcomplexes, as well as stability and moment-preserving properties for the conforming projection operators, we establish the convergence of the resulting nonconforming discretizations of Hodge-Laplace source and eigenvalue problems.

翻译：在本篇文章中,我们研究了Hilbert综合体不兼容的离散性,其中涉及破碎的空间和投影操作员,以保持结构符合离散性;根据对符合基本相容亚复合体的通常假设,以及符合预测操作员的稳定性和瞬时保存特性,我们确定了Hodge-Laplace源和基因价值问题由此产生的不兼容离散性趋同性。