Abstract
We shall study Darcy flow on the heterogeneous system of 3D, 2D, and 1D domains and we present four models for coupling of the flow. For one of these models, we describe in detail its mixed-hybrid formulation. Finally, we show that Schur complements are suitable for solution of the linear system resulting form the lowest order approximation of the mixed-hybrid formulation.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Arbogast, T., Wheeler, M.F., Zhang, N.-Y.: A nonlinear mixed finite element method for a degenerate parabolic equation arising in flow in porous media. SIAM Journal on Numerical Analysis 33(4), 1669–1687 (1996)
Fortin, M., Brezzi, F.: Mixed and Hybrid Finite Element Methods. Springer, Heidelberg (December 1991)
Gerke, H.H., van Genuchten, M.T.: Evaluation of a First-Order water transfer term for variably saturated Dual-Porosity flow models. Water Resources Research 29(4), 1225–1238
Golub, G.H., Van Loan, C.F.: Matrix Computations (Johns Hopkins Studies in Mathematical Sciences, 3rd edn. The Johns Hopkins University Press, Baltimore (October 1996)
Maryška, J., Severýn, O., Vohralík, M.: Numerical simulation of fracture flow with a mixed-hybrid FEM stochastic discrete fracture network model. Computational Geosciences 8(3), 217–234 (2005)
Maryška, J., Rozložník, M., Tůma, M.: Mixed-hybrid finite element approximation of the potential fluid flow problem. J. Comp. Appl. Math. 63, 383–392 (1995)
Maryška, J., Rozložník, M., Tůma, M.: Schur complement systems in the Mixed-Hybrid finite element approximation of the potential fluid flow problem. SIAM J. Sci. Comput. (SISC) 22(2), 704–723 (2000)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2011 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Březina, J., Hokr, M. (2011). Mixed-Hybrid Formulation of Multidimensional Fracture Flow. In: Dimov, I., Dimova, S., Kolkovska, N. (eds) Numerical Methods and Applications. NMA 2010. Lecture Notes in Computer Science, vol 6046. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-18466-6_14
Download citation
DOI: https://doi.org/10.1007/978-3-642-18466-6_14
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-18465-9
Online ISBN: 978-3-642-18466-6
eBook Packages: Computer ScienceComputer Science (R0)