Abstract In this work, we construct and analyze a nonconforming high-order discretization method for the quasi-static single-phase nonlinear poroelasticity problem describing Darcean flow in a deformable porous medium saturated by a slightly compressible fluid. The nonlinear elasticity operator is discretized using a Hybrid High-Order method, while the Darcy operator relies on a Symmetric Weighted Interior Penalty discontinuous Galerkin scheme. The method is valid in two and three space dimensions, delivers an inf-sup stable discretization on general meshes including polyhedral elements and nonmatching interfaces, supports arbitrary approximation orders, and has a reduced cost thanks to the possibility of statically condensing a large subset of the unknowns for linearized versions of the problem. Moreover, the proposed construction can handle both nonzero and vanishing specific storage coefficients.

中文翻译：

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非线性多孔弹性的高阶离散化

摘要 在这项工作中，我们针对准静态单相非线性多孔弹性问题构建并分析了一种非一致性高阶离散化方法，该问题描述了被微压缩流体饱和的可变形多孔介质中的 Darcean 流动。非线性弹性算子使用混合高阶方法离散化，而达西算子依赖于对称加权内部惩罚不连续伽辽金方案。该方法在两个和三个空间维度上都有效，在包括多面体元素和非匹配界面的一般网格上提供 inf-sup 稳定离散化，支持任意近似阶数，并且由于可以静态压缩大量子集的可能性而降低了成本问题的线性化版本的未知数。而且，