Hybridizable discontinuous Galerkin methods for the coupled Stokes–Biot problem
Hybridizable discontinuous Galerkin methods for the coupled Stokes–Biot problem
复制标题
耦合 Stokes Biot 问题的可杂交间断 Galerkin 方法
DOI：
10.1016/j.camwa.2023.05.024
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发表时间：
2023
影响因子：
2.9
通讯作者：
Rhebergen, Sander
中科院分区：
文献类型：
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作者：
Cesmelioglu, Aycil;Lee, Jeonghun J.;Rhebergen, Sander
提出并分析了一种求解耦合Stokes-Biot问题的可杂交间断Galerkin（HDG）有限元方法。特别令人感兴趣的是，离散的速度和位移是H（div）一致的，并满足压缩性方程逐点的元素。此外，在不可压缩极限，离散是强保守的。我们证明了适定性的离散化，并结合后向欧拉时间步进的HDG方法，提出了先验误差估计，证明该方法是免费的体积锁定。数值例子进一步证明了最佳的收敛速度在L2范数的所有未知数和离散是锁定自由。
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 (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.