A mortar finite volume method for a fractured model in porous media

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• 作者：Shuangshuang Chen ; Hongxing Rui ; ^{author.hxrui@sdu.edu.cn}
• 关键词：Fracture model ; The mortar finite volume scheme ; Non-conforming meshes ; Error estimates ; Numerical experiments
• 刊名：Journal of Mathematical Analysis and Applications
• 出版年：2017
• 出版时间：1 April 2017
• 年：2017
• 卷：448
• 期：1
• 页码：707-721
• 全文大小：816 K
• 卷排序：448

文摘

In this paper, we consider a mortar finite volume method for a fractured model of flow in porous media. In this model, the permeability coefficients are variable between the fracture and the surrounding porous media. A finite volume method based on Raviart–Thomas elements combined with the mortar technique of domain decomposition is presented, in which sub-domains are triangulated independently and the meshes do not match at interfaces. The great advantage of the method is avoiding solving the saddle-point problem, since the numerical scheme is just related to the pressure p, and the velocity u can be expressed by p. We also prove error estimates of order h   on the discrete H1H1 norm between the exact solution p and the mortar finite volume solution P   and the (L2)2(L2)2 norm between u and U. Finally, numerical experiments have been performed to show the consistency of the convergence rates with the theoretical analysis.