An Enriched Petrov-Galerkin Method for Darcy Flow in Fractured Porous Media  

作　　者：Huangxin Chen Zixuan Wang 

机构地区：[1]School of Mathematical Sciences and Fujian Provincial Key Laboratory on Mathematical Modeling and High Performance Scientific Computing,Xiamen University,Xiamen,Fujian 361005,China

出　　处：《Annals of Applied Mathematics》2024年第4期346-392,共47页应用数学年刊(英文版)

基　　金：supported by the National Key Research and Development Project of China(Grant No.2023YFA1011702);the NSF of China(Grant No.12122115)。

摘　　要：We develop a locally mass-conservative enriched Petrov-Galerkin(EPG)method without any penalty term for the simulation of Darcy flow in fractured porous media.The discrete fracture model is applied to model the fractures as the lower dimensional fracture interfaces.The new method enriches the approximation trial space of the conforming continuous Galerkin(CG)method with bubble functions and enriches the approximation test space of the CG method with piecewise constant functions in the fractures and the surrounding porous media.We propose a framework for constructing the bubble functions and consider a decoupled algorithm for the EPG method.The solution of the pressure can be decoupled into two steps with a standard CG method and a post-processing correction.The post-processing correction based on the bubble functions in the matrix and the fractures can be solved separately,which is useful for parallel computing.We derive a priori and a posteriori error estimates for the problem.Numerical examples are presented to illustrate the performance of the proposed method.

关 键 词：Discrete fracture model enriched Petrov-Galerkin method local mass conservation POST-PROCESSING error analysis 

分 类 号：O241.82[理学—计算数学]