A residual-based a posteriori error estimator for single-phase Darcy flow in fractured porous media

被引：16
|
作者：
Chen, Huangxin [1 ,2 ,3 ]
Sun, Shuyu [3 ]
机构：
[1] Xiamen Univ, Sch Math Sci, Xiamen 361005, Fujian, Peoples R China
[2] Xiamen Univ, Fujian Prov Key Lab Math Modeling & High Performa, Xiamen 361005, Fujian, Peoples R China
[3] King Abdullah Univ Sci & Technol, Div Phys Sci & Engn, Computat Transport Phenomena Lab, Thuwal 239556900, Saudi Arabia
来源：
NUMERISCHE MATHEMATIK | 2017年 / 136卷 / 03期
关键词：
MIXED FINITE-ELEMENT; EFFICIENT NUMERICAL-MODEL; DISCONTINUOUS GALERKIN; REACTIVE TRANSPORT; FLUID-FLOW; INTERFACES;
D O I：
10.1007/s00211-016-0851-9
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper we develop an a posteriori error estimator for a mixed finite element method for single-phase Darcy flow in a two-dimensional fractured porous media. The discrete fracture model is applied to model the fractures by one-dimensional fractures in a two-dimensional domain. We consider Raviart-Thomas mixed finite element method for the approximation of the coupled Darcy flows in the fractures and the surrounding porous media. We derive a robust residual-based a posteriori error estimator for the problem with non-intersecting fractures. The reliability and efficiency of the a posteriori error estimator are established for the error measured in an energy norm. Numerical results verifying the robustness of the proposed a posteriori error estimator are given. Moreover, our numerical results indicate that the a posteriori error estimator also works well for the problem with intersecting fractures.
引用
收藏
页码：805 / 839
页数：35
相关论文
共 50 条
  • [1] A residual-based a posteriori error estimator for single-phase Darcy flow in fractured porous media
    Huangxin Chen
    Shuyu Sun
    [J]. Numerische Mathematik, 2017, 136 : 805 - 839
  • [2] A RESIDUAL-BASED A POSTERIORI ERROR ESTIMATOR FOR THE STOKES-DARCY COUPLED PROBLEM
    Babuska, Ivo
    Gatica, Gabriel N.
    [J]. SIAM JOURNAL ON NUMERICAL ANALYSIS, 2010, 48 (02) : 498 - 523
  • [3] On a residual-based a posteriori error estimator for the total error
    Papez, Jan
    Strakos, Zdenek
    [J]. IMA JOURNAL OF NUMERICAL ANALYSIS, 2018, 38 (03) : 1164 - 1184
  • [4] A posteriori error estimation of the representer method for single-phase Darcy flow
    Baird, John
    Dawson, Clint
    [J]. COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 2007, 196 (9-12) : 1623 - 1632
  • [5] Benchmarks for single-phase flow in fractured porous media
    Flemisch, Bernd
    Berre, Inga
    Boon, Wietse
    Fumagalli, Alessio
    Schwenck, Nicolas
    Scotti, Anna
    Stefansson, Ivar
    Tatomir, Alexandru
    [J]. ADVANCES IN WATER RESOURCES, 2018, 111 : 239 - 258
  • [6] A residual-based a posteriori error estimator for a fully-mixed formulation of the Stokes-Darcy coupled problem
    Gatica, Gabriel N.
    Oyarzua, Ricardo
    Sayas, Francisco-Javier
    [J]. COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 2011, 200 (21-22) : 1877 - 1891
  • [7] A hybrid-mixed finite element method for single-phase Darcy flow in fractured porous media
    Fu, Guosheng
    Yang, Yang
    [J]. ADVANCES IN WATER RESOURCES, 2022, 161
  • [8] A hybridizable discontinuous Galerkin method on unfitted meshes for single-phase Darcy flow in fractured porous media
    Fu, Guosheng
    Yang, Yang
    [J]. ADVANCES IN WATER RESOURCES, 2023, 173
  • [9] An a posteriori residual-based spatial discretization error estimator for SN neutron transport
    Hart, Nathan H.
    Azmy, Yousry Y.
    Duo, Jose I.
    [J]. ANNALS OF NUCLEAR ENERGY, 2020, 137 (137)
  • [10] Residual-Based A Posteriori Error Estimator for the Mixed Finite Element Approximation of the Biharmonic Equation
    Gudi, Thirupathi
    [J]. NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, 2011, 27 (02) : 315 - 328
12345