### The Influence of Velocity Field Approximations in Tracer Injection Processes

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P. A. Raviart and J. M. Thomas, “A mixed finite element method for second order elliptic problems,” in Lecture Notes in Math (1. Galligani and E. Magenes, eds.), vol. 606, New York, Springer—Verlag, 1977.

F. Brezzi, J. Douglas, and L. D. Marini, “Two families of mixed finite elements for second order elliptic problems,” Numerisehe Mathematik, vol. 47, pp. 217--235, 1985.

F. Brezzi and M. Fortin, Mixed and Hybrid Finite Element Methods. Springer—Verlag, 1991.

J. J. Douglas, R. E. Ewing, and M. F. Wheeler, “The approximation of the pressure by a Mixed—Method in the simulation of miscible displacement,” R.A.I.R.O. Analyse Numerique, vol. 17, pp. 17--33, 1983.

B. L. Darlow, R. E. Ewing, and M. F. Wheeler, “Mixed finite element method for miscible displacement problems in porous media,” SPE Journal, pp. 391--398, 1984.

F. Brezzi, “On the existence, uniqueness and approximation of saddle point problems arising from Lagrange multipliers,” Analyse Numérique/Numerical Analysis (RAIRO), vol. 8(R—2), pp. 129--151, 1974.

M. R. Correa and A. F. D. Loula, “Unconditionally stable mixed finite element methods for Darcy flow,” Computer Methods in Applied Mechanics and Engineering, vol. 197, pp. 1525--1540, 2008.

J. J. Douglas and J. Wang, “An absolutely stabilized finite element method for the Stokes problem,” Math. Comput., vol. 52(186), pp. 495--508, 1989.

A. F. D. Loula, F. A. Rochinha, and M. A. Murad, “Higher—order gradient post—processings for second—order elliptic problems,” Computer Methods in Applied Mechanics and Engineering, vol. 128, pp. 361--381, 1995.

A. Masud and T. J. R. Hughes, “A stabilized finite element method for Darcy flow,” Computer. Methods Appl. Mech. Engrg, vol. 191, pp. 4341--4370, 2002.

G. Barrenechea, L. P. Franca, and F. Valentin, “A Petrov—Galerkin enriched method: A mass conservative finite element method for the Darcy equation,” Computer Methods in Applied Mechanics and Engineering, vol. 196, pp. 2449--2464, 2007.

M. R. Correa and A. F. D. Loula, “Stabilized velocity post—processings for Darcy flow in heterogenous porous media,” Communications in Numerical Methods in Engineering, vol. 23, pp. 461--489, 2007.

I. H. A. da Igreja, Métodos de elementos finitos hibridos estabilizados para escoamentos de Stokes, Darcy e Stokes—Darcy acoplados. PhD thesis, Laboratório Nacional de Computacao Cientifica, Petrépolis, Brasil, 2015.

T. P. Barrios, J. M. Cascén, and M. Gonzalez, “A posteriori error analysis of an augmented mixed finite element method for Darcy flow,” Computer Methods in Applied Mechanics and Engineering, vol. 283, pp. 909--922, 2015.

B. Riviere, Discontinuous Calerkin Methods For Solving Elliptic And Parabolic Equations: Theory and Implementation. Philadelphia, PA, USA: Society for Industrial and Applied Mathematics, 2008.

Y. R. Nunez, Métodos de elementos finitos hibridos aplicados a escoamentos misciveis em meios porosos heterogêneos. PhD thesis, Laboratório Nacional de Computacao Cientifica, Petrépolis, Brasil, 2014.

Y. R. Nunez, C. O. Faria, A. F. D. Loula, and S. M. C. Malta, “A mixe-hybrid finite element method applied to tracer injection processes,” International Journal of Modeling and Simulation for the Petroleum Industry, vol. 6(1), pp. 51-59, 2012.

Y. R. Nunez, C. O. Faria, A. F. D. Loula, and S. M. C. Malta, “A hybrid finite element method applied to miscible displacements in heterogeneous porous media,” Rev. Int. de Métodos Numér. Ca’lc. Diseno Ing., vol. 33(1-2), pp. 45--51, 2017.

S. M. C. Malta, A. F. D. Loula, and E. L. M. Garcia, “Numerical analysis of a stabilized finite element method for tracer injection simulations,” Comput. Methods Appl. Mech. Engrg., vol. 187, pp. 119--136, 2000.

S. M. C. Malta and A. F. D. Loula, “Numerical analysis of finite element

method for miscible displacements in porous media,” Numerical Methods in

Partial Difierential Equations, vol. 14, pp. 519--548, 1998.

M. Abbaszadeh—Dehghani and W. E. Brigham, “Technical report,” Stanford University, 1982.

D. W. Peaceman, Fundamental of Numerical Reservoir Simulation. Elsevier, Amsterdam, 1977.

D. N. Arnold and F. Brezzi, “Mixed and nonconforming finite element

methods: implementation, post—processing and error estimates,” RAIRO

MMAN, vol. 19(7), pp. 7-32, 1985.

R. E. Ewing, J. Wang, and Y. Yang, “A stabilized discontinuous finite element method for elliptic problems,” Numerical Linear Algebra with Applications, vol. 10, pp. 83--104, 2003.

D. N. Arnold, F. Brezzi, B. Cockburn, and L. D. Marini, “Unified analysis

of discontinuous galerkin methods for elliptic problems,” SIAM Journal on

Numerical Analysis, vol. 39(5), pp. 1749--1779, 2002.

I. Harari, “Stability of semidiscrete formulations for parabolic problems at small time steps,” Comput. Methods Appl. Mech. Engrg., vol. 193, pp. 1491--1516, 2004.

A. N. Brooks and T. J. R. Hughes, “Streamline Upwind Petrov—Galerkin Formulations for Convection—Dominated flows with Particular emphasis on the Incompressible Navier—Stokes equations,” Comput. Methods Appl. Mech. Engrg., vol. 32, pp. 199--259, 1982.

A. Datta—Gupta and M. J. King, “A semianalytic approach to tracer flow modeling in heterogeneous permeable media,” Advances in Water Resources, Vol. 18(1)7 pp. 9--24, 1995.

DOI: https://doi.org/10.5540/tema.2018.019.02.347

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