A coupling of nonconforming and mixed finite element methods for Biot's consolidation model
A coupling of nonconforming and mixed finite element methods for Biot's consolidation model
复制标题
DOI：
10.1002/num.21775
复制
发表时间：
2013-09
影响因子：
3.9
通讯作者：
Son-Young Yi
中科院分区：
文献类型：
--
作者：
Son-Young Yi
本文发展了求解毕奥固结模型的混合有限元法。特别是，这项工作的动机是克服非物理振荡的压力变量，这是已知的锁定在孔隙弹性。该方法是基于一个耦合的三维有限元方法的固相的位移与一个标准的混合有限元方法的流体相的压力和速度。通过在离散变分公式中增加一个跳跃项，得到了离散Korn不等式。我们证明了半离散和全离散格式的先验误差估计的严格证明。最佳误差估计已被导出。特别是，最优的压力，在不同的规范，已被证明为两种情况下，当约束的特定的存储系数C0是严格的积极的，当C0是非负的。数值结果验证了该方法的准确性，也表明了该方法克服非物理压力振荡的有效性。© 2013 Wiley Periodicals，Inc. Numer Methods Partial Differential Eq，2013
In this article, we develop a nonconforming mixed finite element method to solve Biot's consolidation model. In particular, this work has been motivated to overcome nonphysical oscillations in the pressure variable, which is known as locking in poroelasticity. The method is based on a coupling of a nonconforming finite element method for the displacement of the solid phase with a standard mixed finite element method for the pressure and velocity of the fluid phase. The discrete Korn's inequality has been achieved by adding a jump term to the discrete variational formulation. We prove a rigorous proof of a‐priori error estimates for both semidiscrete and fully‐discrete schemes. Optimal error estimates have been derived. In particular, optimality in the pressure, measured in different norms, has been proved for both cases when the constrained specific storage coefficient c0 is strictly positive and when c0 is nonnegative. Numerical results illustrate the accuracy of the method and also show the effectiveness of the method to overcome the nonphysical pressure oscillations. © 2013 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2013