Mixed-hybrid FEM discrete fracture network model of the fracture flow

  • J. Maryška
  • O. Severýn
  • M. Vohralík
Conference paper


A stochastic discrete fracture network model of Darcy’s underground water flow in disrupted rock massifs is introduced. The mixed finite element method and hybridization of the appropriate lowest order Raviart-Thomas approximation are used for the special conditions of a flow through a connected system of 2D polygons embedded in 3D. A model problem is tested.


Model Problem Fracture Flow Pressure Trace Mixed Finite Element Method Type Boundary Condition 


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  1. [1]
    Maryška, J., Rozložník, M., Tůma, M. (2000): Schur complement reduction in the mixed-hybrid finite element approximation of Darcy’s law: rounding error analysis. J. Comput. Appl. Math. 117, 159–173MathSciNetMATHCrossRefGoogle Scholar
  2. [2]
    Quarteroni, A., Valli, A. (1994): Numerical approximation of partial differential equations. Springer, BerlinMATHGoogle Scholar
  3. [3]
    Raviart, P.A., Thomas, J.M. (1977): A mixed finite element method for 2nd order elliptic problems. In: Galligani, I., Magenes, E. (eds.) Mathematical aspects of finite element methods. (Lecture Notes in Mathematics, vol. 606) Springer, Berlin, pp. 292–315CrossRefGoogle Scholar
  4. [4]
    Roberts, J.E., Thomas, J.-M. (1991): Mixed and hybrid methods. In: Ciarlet, P.G., Lions, J.-L. (eds.) Handbook of numerical analysis, Vol. II. Finite element methods. Part 1. North-Holland, Amsterdam, pp. 523–639Google Scholar
  5. [5]
    Vohralík, M. (2001): Existence-and error-analysis of the mixed-hybrid model of the fracture flow. Preprint MATH-NM-06-2001. Technische Universität Dresden, DresdenGoogle Scholar

Copyright information

© Springer-Verlag Italia 2003

Authors and Affiliations

  • J. Maryška
    • 1
  • O. Severýn
    • 2
  • M. Vohralík
    • 3
  1. 1.Department of Modeling of Processes, Faculty of MechatronicsTechnical University of LiberecLiberecCzech Republic
  2. 2.Faculty of MechatronicsTechnical University of LiberecLiberecCzech Republic
  3. 3.Czech Technical UniversityFNPEPrahaCzech Republic

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