Mixed-hybrid finite elements for saturated groundwater flow
bookPart
An accurate approximation of the specific discharge (Darcy velocity) is crucial in the numerical solution of a variety of groundwater flow problems. In approximating the specific discharge q by standard finite difference or finite element techniques, first an approximation of the piezometric head (potential) φ is determined as a set of cell averages, nodal values or piecewise smooth functions. This approximation of φ is then numerically differentiated and multiplied by the often rough tensor of hydraulic conductivity (permeability) K to obtain an approximation of q. In a physical context it is desirable to obtain an approximation of q, that fulfils the continuity equation as well as possible with respect to the finite difference grid or finite element mesh. Such an approximation can be determined by the mixed finite element method. The mixed finite element method results in a large system of linear equations. The choice of a numerical method to solve this system is restricted by the fact that its coefficient matrix is indefinite. This drawback can be circumvented by an implementation technique called hybridization, which leads to a symmetric positive definite system of linear equations. Since this system is sparse, it can be solved efficiently by the preconditioned conjugate gradient method.
Topics
TNO Identifier
231280
ISBN
038752701X
Publisher
Springer-Verlag Berlin
Source title
Proceedings of the 8th International Conference on Computational Methods in Water Resources, 11 June 1990 through 15 June 1990, Venice, Italy
Editor(s)
Gambolati, G.
Rinaldo, A.
Brebbia, C.A.
Gray, W.G.
Pinder, G.F.
Rinaldo, A.
Brebbia, C.A.
Gray, W.G.
Pinder, G.F.
Place of publication
Berlin
Pages
17-22
Files
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