Burman Erik, Hansbo Peter, Larson Mats G, Samvin David
1Mathematics, University College London, London, UK.
2Mechanical Engineering, Jönköping University, Jönköping, Sweden.
GEM. 2019;10(1):10. doi: 10.1007/s13137-019-0120-z. Epub 2019 Jan 29.
We propose an unfitted finite element method for flow in fractured porous media. The coupling across the fracture uses a Nitsche type mortaring, allowing for an accurate representation of the jump in the normal component of the gradient of the discrete solution across the fracture. The flow field in the fracture is modelled simultaneously, using the average of traces of the bulk variables on the fractures. In particular the Laplace-Beltrami operator for the transport in the fracture is included using the average of the projection on the tangential plane of the fracture of the trace of the bulk gradient. Optimal order error estimates are proven under suitable regularity assumptions on the domain geometry. The extension to the case of bifurcating fractures is discussed. Finally the theory is illustrated by a series of numerical examples.
我们提出了一种用于裂隙多孔介质中流动的非拟合有限元方法。跨裂隙的耦合采用了Nitsche型 mortar 方法，能够精确表示离散解梯度的法向分量在裂隙处的跳跃。裂隙中的流场同时进行建模，使用裂隙上整体变量迹线的平均值。特别地，通过整体梯度迹线在裂隙切平面上投影的平均值来包含裂隙中输运的拉普拉斯 - 贝尔特拉米算子。在对区域几何形状的适当正则性假设下证明了最优阶误差估计。讨论了该方法向分叉裂隙情况的扩展。最后通过一系列数值例子对理论进行了说明。
