论文标题
耦合Stokes的混合杂交不连续的Galerkin方法 - -biot问题
Hybridizable discontinuous Galerkin methods for the coupled Stokes--Biot problem
论文作者
论文摘要
我们为耦合的stokes问题提供并分析了一种可杂交的不连续盖素（HDG）有限元方法 - 二元问题。特别有趣的是，离散的速度和位移是$ h（\ text {div}）$ - 符合元素上的压缩性方程式并满足元素上的压缩性方程。此外，在不可压缩的限制下，离散化非常保守。我们证明了离散化的良好性，并在将HDG方法与向后的Euler Time步进后结合后，提出了先验错误估计，该错误估计表明该方法没有容积锁定。数值示例进一步证明了所有未知数的$ l^2 $ norm中的最佳收敛速率，并且离散化无锁定。
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.
