发表机构
Shenzhen University of Information Technology; Morgan State University; Southern University of Science and Technology（深圳信息技术大学; 摩根州立大学; 南方科技大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文针对基于旋转的 Biot 系统混合有限元离散，通过圆周质量集中与相容离散复形，证明单元压力单调性并抑制压力振荡。
AI 中文摘要
我们建立了基于旋转的 Biot 系统混合有限元离散格式的单元压力单调性。空间离散基于相容的离散 de Rham 复形，对旋转、位移、达西通量和压力采用标准最低阶元。时间离散采用向后欧拉方法。离散复形的精确性将力学对压力 Schur 补的贡献约化为一个缩放的压力的质量矩阵，从而产生正的对角力学容量。对于达西部分，正的圆周面权重在通量消去后产生一个加权单元图拉普拉斯算子，而质量集中乘积仍与标准达西乘积一致等价。对角力学容量和加权单元图拉普拉斯算子使凝聚后的压力矩阵为 Stieltjes 型。因此，压力传播子逐项非负，从而得到单元离散最大值原理。数值实验证实了预期的收敛阶，并表明所提出的离散格式抑制了虚假的单元压力振荡。
英文摘要
We establish cellwise pressure monotonicity for a mixed finite element discretization of the rotation-based Biot system. The spatial discretization is based on compatible discrete de Rham complexes, using standard lowest-order elements for rotation, displacement, Darcy flux, and pressure. For the temporal discretization, we employ the backward Euler method. Exactness of the discrete complexes reduces the mechanics contribution to the pressure Schur complement to a scaled pressure mass matrix, yielding a positive diagonal mechanics capacity. For the Darcy part, positive circumcentric facet weights yield a weighted cell graph Laplacian after flux elimination, while the mass-lumped product remains uniformly equivalent to the standard Darcy product. The diagonal mechanics capacity and the weighted cell graph Laplacian make the condensed pressure matrix Stieltjes. Consequently, the pressure propagator is entrywise nonnegative, which yields a cellwise discrete maximum principle. Numerical experiments confirm the predicted convergence rates and show that the proposed discretization suppresses spurious cellwise pressure oscillations.
