论文标题
锁定一般多边形网格上的毛弹性生物系统的交错DG方法
Locking free staggered DG method for the Biot system of poroelasticity on general polygonal meshes
论文作者
论文摘要
在本文中，我们提出和分析了一种不连续的盖尔金方法，用于在一般多边形网格上使用孔弹性的生物弹性制度的五场配方。弹性配备了应力 - 置换式反转配方，并具有弱应力对称性的任意多项式顺序，该阶延伸了（L. Zhao和E.-J. Park，SiamJ.Sci。42（2020），A2158-A2181）。所提出的方法是免费锁定的，并且可以处理可能包括悬挂节点的高度扭曲的网格，这对于实际应用是可取的。我们证明了半分化方案的收敛估计以及其自然规范中所有变量的完全离散方案。特别是，稳定性和收敛分析不需要统一的积极积极系数。此外，为了减少全球系统的大小，我们提出了一种基于五场配方的固定应力分裂方案，在该方案中证明了该方案的线性收敛性。进行了几个数值实验，以确认所提出方法的最佳收敛速率和无锁定属性。
In this paper we propose and analyze a staggered discontinuous Galerkin method for a five-field formulation of the Biot system of poroelasticity on general polygonal meshes. Elasticity is equipped with stress-displacement-rotation formulation with weak stress symmetry for arbitrary polynomial orders, which extends the piecewise constant approximation developed in (L. Zhao and E.-J. Park, SIAM J. Sci. Comput. 42 (2020), A2158-A2181). The proposed method is locking free and can handle highly distorted grids possibly including hanging nodes, which is desirable for practical applications. We prove the convergence estimates for the semi-discrete scheme and fully discrete scheme for all the variables in their natural norms. In particular, the stability and convergence analysis do not need a uniformly positive storativity coefficient. Moreover, to reduce the size of the global system, we propose a five-field formulation based fixed stress splitting scheme, where the linear convergence of the scheme is proved. Several numerical experiments are carried out to confirm the optimal convergence rates and the locking-free property of the proposed method.
