## Abstract

An accurate mixed finite element method to solve both flow and transport is developed for stochastic simulations of transportin saturated aquifers characterized by random log-hydraulic conductivity fields. The main advantage of the mixed finiteelement is that it is local mass conservative. Unlike in stochastic finite element methods, this approach yields concentrationfields and concentration moments for samples of the random field. In this way, it will be possible t o analyze the behavior ofdifferent ensemble average observables of the transport process as well as the behavior of their fluctuations. Results of thestochastic simulations described here can be used to assess the reliability for real cases of the ensemble average quantitiesprovided by stochastic modeling of transport in groundwater.

## Authors

Florin A. **Radu
**UFZ – Helmholtz Center for Environmental Research, Permoserstr. 15, D-04318 Leipzig, Germany

University of Jena, Wöllnitzerstr. 7, D-07749 Jena, Germany

Nicolae **Suciu
**Department of Mathematics, Chair for Applied Mathematics I, University of Erlangen-Nuremberg

Tiberiu Popoviciu Institute of Numerical Analysis, Romanian Academy

## Keywords

## Cite this paper as:

F.A. Radu, N. Suciu, *Stochastic simulations based on mixed finite elements for solute transport in groundwater*, Proc. Appl. Math. Mech., 9 (2009), 19-22

doi: 10.1002/pamm.200910006

## References

see the expansion block below

soon

## About this paper

##### Print ISSN

Not available yet.

##### Online ISSN

Not available yet.

##### Google Scholar Profile

google scholar link

[1] P. Bastian, K. Birken, K. Johanssen, S. Lang, N. Neuss, H. Rentz-Reichert, C. Wieners, *UG–a flexible toolboxfor solving partial differential equations*, Comput. Visualiz. Sci. 1 (1997), pp. 27-40.

[2] P.R. Kramer,O. Kurbanmuradov, K. Sabelfeld, *Comparative analysis of multiscale Gaussian random field simulation algorithms*, J. Comp. Phys. 226, pp. 897-924 (2007).

CrossRef (DOI)

[3] F. A. Radu, I.S. Pop, P. Knabner, *Order of convergence estimates for an Euler implicit, mixed finite element discretization of Richards’ equation*, SIAMJ.Numer.Anal.42, pp. 1452-1478 (2004).

CrossRef (DOI)

[4] F.A. Radu, I.S.Pop, P. Knabner, *Error estimates for a mixed finite element discretization of some degenerate parabolic equations*, Numer. Math. 109 (2), pp. 285-311 (2008).

CrossRef (DOI)

[5] F.A. Radu,M. Bause,A. Prechtel, S. Attinger, *A mixed hybrid finite element discretization scheme for reactive transport in porous media*, Numerical Mathematics and Advanced Applications, K. Kunisch, G. Of and O. Steinbach (editors), Springer Verlag,Heidelberg (2008), pp. 513-520.

CrossRef (DOI)

[6] F.A. Radu, I.S. Pop, S. Attinger, *Analysis of an Euler implicit – mixed finite element scheme for reactive solute transport in porous media*, Numerical Methods Partial Differential Equations, (2009).

CrossRef (DOI)

[7] K. Sabelfeld, *Monte Carlo Methods in Boundary Value Problems*, Springer, Berlin (1991).

[8] N. Suciu,C.Vamos, J. Vanderborght, H. Hardelauf, H. Vereecken, *Numerical investigations on ergodicity of solute transport in heterogeneous aquifers*, Water Resour. Res. 42, W04409, (2006).

CrossRef (DOI)

[9] N. Suciu, C.Vamos, H.Vereecken, K.Sabelfeld, P. Knabner, *Memory effects induced by dependence on initial conditions and ergodicity of transport in heterogeneous media*, Water Resour. Res. 44, W08501, (2008).

CrossRef (DOI)

[10] A. M. Yaglom, *Correlation Theory of Stationary and Related Random Functions*, Volume I: Basic Results, Springer-Verlag, NewYork (1987).

soon