论文标题
分析Biot合并模型的嵌入式杂交不连续的Galerkin方法
Analysis of an embedded-hybridizable discontinuous Galerkin method for Biot's consolidation model
论文作者
论文摘要
我们提出了一种可用于准静态孔隙弹性模型的总压力公式的可嵌入的杂交不连续的Galerkin有限元法。尽管位移和达西速度通过不连续的多项式近似，但$ h（\ text {div}）$ - 这些未知数的符合性由lagrange倍增器强制执行。半混凝土问题表明是稳定的，并且完全离散的问题被证明是良好的。此外，得出了时空的先验误差估计，并通过数值示例确认，这表明所提出的离散化没有体积锁定。
We present an embedded-hybridizable discontinuous Galerkin finite element method for the total pressure formulation of the quasi-static poroelasticity model. Although the displacement and the Darcy velocity are approximated by discontinuous piece-wise polynomials, $H(\text{div})$-conformity of these unknowns is enforced by Lagrange multipliers. The semi-discrete problem is shown to be stable and the fully discrete problem is shown to be well-posed. Additionally, space-time a priori error estimates are derived, and confirmed by numerical examples, that show that the proposed discretization is free of volumetric locking.
