耦合Stokes--Biot问题的可杂交间断Galerkin方法
Hybridizable discontinuous Galerkin methods for the coupled Stokes--Biot problem
AI总结：
本文提出并分析了耦合Stokes--Biot问题的可杂交间断Galerkin有限元方法，证明了其适定性和无体积锁定性质，并通过数值实验验证了所有未知量的最优收敛阶。
AI中文摘要：
我们提出并分析了一种用于耦合Stokes--Biot问题的可杂交间断Galerkin（HDG）有限元方法。特别值得关注的是，离散速度和位移是$H(\ ext{div})$-协调的，并且在单元上逐点满足可压缩性方程。此外，在不可压缩极限下，该离散格式是强守恒的。我们证明了该离散格式的适定性，并在将HDG方法与向后Euler时间步进结合后，给出了先验误差估计，表明该方法不存在体积锁定。数值算例进一步表明，所有未知量在$L^2$-范数下均达到最优收敛阶，且该离散格式无锁定。
英文摘要：
We present and analyze a hybridizable discontinuous Galerkin (HDG) finite element method for the coupled Stokes--Biot problem. Of particular interest is that the discrete velocities and displacement are $H(\text{div})$-conforming and satisfy the compressibility equations pointwise on the elements. Furthermore, in the incompressible limit, the discretization is strongly conservative. We prove well-posedness of the discretization and, after combining the HDG method with backward Euler time stepping, present a priori error estimates that demonstrate that the method is free of volumetric locking. Numerical examples further demonstrate optimal rates of convergence in the $L^2$-norm for all unknowns and that the discretization is locking-free.
