Research Interests

My research interests are in the numerical analysis and solution of partial differential equations and large scale scientific computing with applications to fluid flow and transport. My current research focus is on the design and analysis of accurate multiscale adaptive discretization techniques (mixed finite elements, finite volumes, finite differences) and efficient linear and nonlinear iterative solvers (domain decomposition, multigrid, Newton-Krylov methods) for massively parallel simulations of coupled multiphase porous media and surface flows. Other areas of research interest include estimation of uncertainty in stochastic systems and mathematical and computational modeling for biomedical applications.

Ph.D. Thesis

Mixed Finite Element Methods for Flow in Porous Media, Technical Report TR96-09, Dept. Comp. Appl. Math., Rice University and Technical Report TICAM 96-23, University of Texas at Austin.

Selected publications

T.-T.-P. Hoang and I. Yotov, A space-time mixed finite element method for reduced fracture flow models on nonmatching grids; submitted;

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    • W. M. Boon, D. Gläser, R. Helmig, K. Weishaupt, and I. Yotov, A mortar method for the coupled Stokes-Darcy problem using the MAC scheme for Stokes and mixed finite elements for Darcy, Computational Geosciences (2024); https://doi.org/10.1007/s10596-023-10267-6

    S. Caucao, T. Li, and I. Yotov, An augmented fully-mixed formulation for the quasistatic Navier-Stokes-Biot model, IMA Journal of Numerical Analysis (2023); https://doi.org/10.1093/imanum/drad036
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    • W. M. Boon, D. Gläser, R. Helmig, and I. Yotov, Flux-mortar mixed finite element methods with multipoint flux approximation, Computer Methods in Applied Mechanics and Engineering 405 (2023) 115870; https://doi.org/10.1016/j.cma.2022.115870
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    • V. Anaya, R. Caraballo, S. Caucao, L. F. Gatica, R. Ruiz-Baier, and I. Yotov, A vorticity-based mixed formulation for the unsteady Brinkman–Forchheimer equations, Computer Methods in Applied Mechanics and Engineering, 404 (2023), pp. 115829; https://doi.org/10.1016/j.cma.2022.115829
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    • M. Jayadharan, M. Kern, M. Vohralík, and I. Yotov, A space-time multiscale mortar mixed finite element method for parabolic equations, SIAM Journal on Numerical Analysis, 61:2 (2023), pp. 675-706; https://doi.org/10.1137/21M1447945
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    • S. Caucao, R. Oyarzúa, S Villa-Fuentes, I. Yotov, A three-field Banach spaces-based mixed formulation for the unsteady Brinkman-Forchheimer equations, Computer Methods in Applied Mechanics and Engineering, 394 (2022), pp. 114895; https://doi.org/10.1016/j.cma.2022.114895
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    • S. Caucao, T. Li, and I. Yotov, A multipoint stress-flux mixed finite element method for the Stokes-Biot model, Numerische Mathematik 152 (2022), pp. 411-473; https://doi.org/10.1007/s00211-022-01310-2
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    • W. M. Boon, D. Gläser, R. Helmig, and I. Yotov, Flux-mortar mixed finite element methods on non-matching grids, SIAM Journal on Numerical Analysis, 60:3 (2022), pp. 1193-1225; https://doi.org/10.1137/20M1361407
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    • T. Li and I. Yotov, A mixed elasticity formulation for fluid–poroelastic structure interaction, ESAIM: Mathematical Modelling and Numerical Analysis (M2AN), 56 (2022) pp. 1-40; https://doi.org/10.1051/m2an/2021083

    R. Ruiz-Baier, M. Taffetani, H. D. Westermeyer, and I. Yotov, The Biot-Stokes coupling using total pressure: formulation, analysis and application to interfacial flow in the eye, Computer Methods in Applied Mechanics and Engineering, 389 (2022) pp. 114384; https://doi.org/10.1016/j.cma.2021.114384
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    • M. Jayadharan, E. Khattatov, and I. Yotov, Domain decomposition and partitioning methods for mixed finite element discretizations of the Biot system of poroelasticity, Computational Geosciences (2021) 25, pp. 1919-1938; https://doi.org/10.1007/s10596-021-10091-w
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    • J. Both, I. S. Pop, and I. Yotov, Global existence of a weak solution to unsaturated poroelasticity, ESAIM: Mathematical Modelling and Numerical Analysis (M2AN), 55 (2021), pp. 2849-2897; https://doi.org/10.1051/m2an/2021063

    I. Ambartsumyan, E. Khattatov, J. M. Nordbotten, and I. Yotov, A multipoint stress mixed finite element method for elasticity on quadrilateral grids, Numerical Methods for Partial Differential Equations, 37:3 (2021), pp. 1886-1915; https://doi.org/10.1002/num.22624
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    • S. Caucao and I. Yotov, A Banach space mixed formulation for the unsteady Brinkman-Forchheimer equations, IMA Journal of Numerical Analysis, 41:4 (2021), pp. 2708–2743; https://doi.org/10.1093/imanum/draa035

    I. Ambartsumyan, E. Khattatov, and I. Yotov, A coupled multipoint stress - multipoint flux mixed finite element method for the Biot system of poroelasticity, Computer Methods in Applied Mechanics and Engineering, 372 (2020), pp. 113407; https://doi.org/10.1016/j.cma.2020.113407
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    • I. Ambartsumyan, E. Khattatov, J. M. Nordbotten, and I. Yotov, A multipoint stress mixed finite element method for elasticity on simplicial grids, SIAM Journal on Numerical Analysis, 58:1 (2020), pp. 630--656; https://doi.org/10.1137/18M1229183
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    • I. Ambartsumyan, E. Khattatov, C. Wang, and I. Yotov, Stochastic multiscale flux basis for Stokes-Darcy flows, Journal of Computational Physics, 401 (2020) 109011; https://doi.org/10.1016/j.jcp.2019.109011
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    • I. Ambartsumyan, V. J. Ervin, T. Nguyen, and I. Yotov, A nonlinear Stokes-Biot model for the interaction of a non-Newtonian fluid with poroelastic media, ESAIM: Mathematical Modelling and Numerical Analysis (M2AN), 53 (2019), pp. 1915–1955; https://doi.org/10.1051/m2an/2019061
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    • E. Khattatov and I. Yotov, Domain decomposition and multiscale mortar mixed finite element methods for linear elasticity with weak stress symmetry, ESAIM: Mathematical Modelling and Numerical Analysis (M2AN), 53 (2019), pp. 2081–2108; https://doi.org/10.1051/m2an/2019057
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    • I. Ambartsumyan, E. Khattatov, J. Lee, and I. Yotov, Higher order multipoint flux mixed finite element methods on quadrilaterals and hexahedra, Mathematical Models and Methods in Applied Sciences (M3AS), 29:6 (2019), pp. 1037-1077; http://dx.doi.org/10.1142/S0218202519500167
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    • I. Ambartsumyan, E. Khattatov, T. Nguyen, and I. Yotov, Flow and transport in fractured poroelastic media, International Journal on Geomathematics 10:1 (2019), pp. 1-34; https://doi.org/10.1007/s13137-019-0119-5
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    • W. Boon, J. Nordbotten, and I. Yotov, Robust discretization of flow in fractured porous media, SIAM J. Numer. Anal. 56:4 (2018), pp. 2203-2233.
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    • I. Ambartsumyan, E. Khattatov, I. Yotov, and P. Zunino, A Lagrange multiplier method for a Stokes-Biot fluid-poroelastic structure interaction model, Numerische Mathematik 140 (2018), pp. 513–553
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    • M. Bukac, I. Yotov, and P. Zunino, Dimensional model reduction for flow through fractures in poroelastic media, ESAIM: Mathematical Modelling and Numerical Analysis (M2AN) 51 (2017), pp 1429-1471.
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    • B. Ganis, D. Vassilev, C. Wang, and I. Yotov, A multiscale flux basis for mortar mixed discretizations of Stokes-Darcy flows, Computer Methods in Applied Mechanics and Engineering, 313 (2017), pp. 259–278.
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    • O. Al-Hinai, M. F. Wheeler, and I. Yotov, A generalized mimetic finite difference method and two-point flux schemes over Voronoi diagrams, ESAIM: Mathematical Modelling and Numerical Analysis (M2AN), 51 (2017), pp. 679-706.
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    • J. Barber, R. Tanase, and I. Yotov, Kalman filter parameter estimation for a nonlinear diffusion model of epithelial cell migration using stochastic collocation and the Karhunen-Loeve expansion, Mathematical Biosciences, 276 (2016), pp. 133-144.
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    • M. Bukac, I. Yotov, and P. Zunino, An operator-splitting approach for the interaction between a fluid and a multilayered poroelastic structure, Numerical Methods for Partial Differential Equations, 31 (2015), pp. 1054–1100.
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    • M. Bukac, I. Yotov, R. Zakerzadeh, and P. Zunino, Partitioning strategies for the interaction of a fluid with a poroelastic material based on a Nitsche's coupling approach, to Computer Methods in Applied Mechanics and Engineering, 292 (2015), pp. 138-170.
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    • B. Ganis, K. Kumar, G. Pencheva, M. F. Wheeler, and I. Yotov, A multiscale mortar method and two-stage preconditioner for multiphase flow using a global Jacobian approach, SPE Large Scale Computing and Big Data Challenges in Reservoir Simulation Conference, SPE 172990-MS (2014).
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    • B. Ganis, K. Kumar, G. Pencheva, M. F. Wheeler, and I. Yotov, A global Jacobian method for mortar discretizations of a fully-implicit two-phase flow model, Multiscale Modeling and Simulation, 12:4 (2014), pp. 1401-1423.
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    • D. Vassilev, C. Wang, and I. Yotov, Domain decomposition for coupled Stokes and Darcy flows, Computer Methods in Applied Mechanics and Engineering, 268 (2014), pp. 264-283.
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    • V. Girault, D. Vassilev, and I. Yotov, Mortar multiscale finite element methods for Stokes-Darcy flows, Numerische Mathematik 127 (2014), pp 93-165.
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    • A. Arraras, L. Portero, and I. Yotov, Error analysis of multipoint flux domain decomposition methods for evolutionary diffusion problems, Journal of Computational Physics, 257 (2014), pp. 1321-1351.
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    • K. Lipnikov, D. Vassilev and I. Yotov, Discontinuous Galerkin and Mimetic Finite Difference Methods for Coupled Stokes-Darcy Flows on Polygonal and Polyhedral Grids, Numerische Mathematik, 126 (2014), pp. 321-360.
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    • M. F. Wheeler, G. Xue, and I. Yotov, Coupling multipoint flux mixed finite element methods with continuous Galerkin methods for poroelasticity, Computational Geosciences, 18 (2014) pp. 57-75.
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    • B. Ganis, M. Juntunen, G. Pencheva, M. F. Wheeler, and I. Yotov, A global Jacobian method for mortar discretizations of nonlinear porous media flows, SIAM J. Scientific Computing, 36, (2014) pp. A522-A542.
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    • J. Barber, M. Tronzo, C. Horvat, G. Clermont, J. Upperman, Y. Vodovotz, and I. Yotov, A three-dimensional mathematical and computational model of necrotizing enterocolitis, J. Theoretical Biology, 322 (2013) pp. 17-32.
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    • R. Liu, M. F. Wheeler, and I. Yotov, On the Spatial Formulation of Discontinuous Galerkin Methods for Finite Elastoplasticity, Computer Methods in Applied Mechanics and Engineering, 253 (2013) pp. 219-236.
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    • M. F. Wheeler, G. Xue, and I. Yotov, Accurate Cell-Centered Discretizations for Modeling Multiphase Flow in Porous Media on General Hexahedral and Simplicial Grids, SPE Journal, 17:3 (2012) pp. 779-793.
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    • B. Ganis, G. Pencheva, M. F. Wheeler, T. Wildey, and I. Yotov, A Frozen Jacobian Multiscale Mortar Preconditioner for Nonlinear Interface Operators, Multiscale Modeling and Simulation, 10:3 (2012) pp. 853-873.
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    • M. F. Wheeler, G. Xue, and I. Yotov, A Multipoint Flux Mixed Finite Element Method on Distorted Quadrilaterals and Hexahedra, Numerische Mathematik, 121 (2012) pp. 165-204.
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    • M. F. Wheeler, G. Xue, and I. Yotov, A Multiscale Mortar Multipoint Flux Mixed Finite Element Method, ESAIM: Mathematical Modelling and Numerical Analysis (M2AN), 46:4 (2012) pp. 759-796.
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    • M. F. Wheeler, G. Xue, and I. Yotov, Local Velocity Postprocessing for Multipoint Flux Methods on General Hexahedra , International Journal of Numerical Analysis and Modeling, 9:3 (2012) pp. 607-627.
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    • B. Ganis, I. Yotov, and M. Zhong, A Stochastic Mortar Mixed Finite Element Method for Flow in Porous Media with Multiple Rock Types, SIAM J. Sci. Comp. 33:3 (2011) 1439-1474.
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    • M. F. Wheeler, T. Wildey, and I. Yotov, A multiscale preconditioner for stochastic mortar mixed finite elements,Comp. Meth. in Appl. Mech. and Engng. 200 (2011) 1251-1262.
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    • R. Ingram, M. F. Wheeler, and I. Yotov, A multipoint flux mixed finite element method on hexahedra, SIAM J. Numer. Anal., 48:4 (2010) 1281-1312.
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    • B. Ganis and I. Yotov, Implementation of a Mortar Mixed Finite Element Method using a Multiscale Flux Basis, Comp. Meth. in Appl. Mech. and Engng., 198 (2009) 3989-3998.
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    • D. Vassilev and I. Yotov, Coupling Stokes-Darcy flow with transport, SIAM J. Sci. Comp., 31:5 (2009) 3661-3684.
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    • K. Lipnikov, M. Shashkov, and I. Yotov, Local flux mimetic finite difference methods, Numerische Mathematik, 112:1 (2009), 115-152.
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    • B. Ganis, H. Klie, M. F. Wheeler, T. Wildey, I. Yotov, and D. Zhang, Stochastic collocation and mixed finite elements for flow in porous media, Comp. Meth. in Appl. Mech. and Engng., 197 (2008) 3547-3559.
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    • G. Pencheva and I. Yotov, Interior superconvergence in mortar and non-mortar mixed finite element methods on non-matching grids, Comp. Meth. in Appl. Mech. and Engng., 197 (2008) 4307-4318.
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    • V. Girault, S. Sun, M. F. Wheeler, and I. Yotov, Coupling Discontinuous Galerkin and Mixed Finite Element Discretizations using Mortar Finite Elements, SIAM J. Numer. Anal. 46:2 (2008) 949-979.
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    • I. Aavatsmark, G.T. Eigestad, R.A. Klausen, M. F. Wheeler and I. Yotov, Convergence of a symmetric MPFA method on quadrilateral grids, Computational Geosciences 11 (2007) 333-345.
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    • T. Arbogast, G. Pencheva, M. F. Wheeler, and I. Yotov, A multiscale mortar mixed finite element method, Multiscale Modeling and Simulation, 6:1 (2007) 319-346.
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    • T. F. Russell, M. F. Wheeler and I. Yotov, Superconvergence for control-volume mixed finite element methods on rectangular grids, SIAM J. Numer. Anal. 45:1 (2007) 223-235.
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    • M. F. Wheeler and I. Yotov, A multipoint flux mixed finite element method, SIAM J. Numer. Anal. 44:5 (2006) 2082-2106.
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    • M. Berndt, K. Lipnikov, M. Shashkov, M. F. Wheeler, and I. Yotov, A mortar mimetic finite difference method on non-matching grids, Numerische Mathematik 102:2 (2005) 203-230.
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    • M. F. Wheeler and I. Yotov, A posteriori error estimates for the mortar mixed finite element method, SIAM J. Numer. Anal. 43:3 (2005) 1021-1042.
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    • M. Berndt, K. Lipnikov, M. Shashkov, M. F. Wheeler, and I. Yotov, Superconvergence of the velocity in mimetic finite difference methods on quadrilaterals, SIAM J. Numer. Anal. 43:4 (2005) 1728-1749.
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    • B. Riviere and I. Yotov, Locally Conservative Coupling of Stokes and Darcy Flows, SIAM J. Numer. Anal. 42:5 (2005) 1959-1977.
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    • W. J. Layton, F. Schieweck, and I. Yotov, Coupling fluid flow with porous media flow, SIAM J. Numer. Anal. 40:6 (2003) 2195-2218.
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    • G. Pencheva and I. Yotov, Balancing domain decomposition for mortar mixed finite element methods on non-matching grids, Numer. Linear Algebra Appl. 10:1-2 (2003) 159-180.
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    • J. A. Wheeler, M. F. Wheeler, and I. Yotov, Enhanced velocity mixed finite element methods for flow in multiblock domains, Computational Geosciences 6:3-4 (2002) 315-332.
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    • M. Peszynska, M. F. Wheeler, and I. Yotov, Mortar upscaling for multiphase flow in porous media, Computational Geosciences 6:1 (2002) 73-100.
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    • I. Yotov, A multilevel Newton-Krylov interface solver for multiphysics couplings of flow in porous media, Numer. Linear Algebra Appl. 8 (2001) 551-570.
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    • T. Kearsley, L. C. Cowsar, R. Glowinski, M. F. Wheeler, and I. Yotov, New optimization approach to multiphase flow, J. Optim. Theory Appl. 111 (2001) 473-488.
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    • I. Yotov, Interface solvers and preconditioners of domain decomposition type for multiphase flow in multiblock porous media, Advances in Computation: Theory and Practice, vol. 7 (2001) 157-167.
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    • T. Arbogast, L. C. Cowsar, M. F. Wheeler, and I. Yotov, Mixed finite element methods on non-matching multiblock grids , SIAM J. Numer. Anal. 37:4 (2000) 1295-1315
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    • M. F. Wheeler and I. Yotov, Multigrid on the interface for mortar mixed finite element methods for elliptic problems, Comp. Meth. in Appl. Mech. and Engng. 184 (2000) 287-302.
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    • M. F. Wheeler, T. Arbogast, S. Bryant, J. Eaton, Q. Lu, M. Peszynska and I. Yotov, A parallel multiblock/multidomain approach to reservoir simulation, Fifteenth SPE Symposium on Reservoir Simulation (1999) 51-62.
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    • M. F. Wheeler and I. Yotov, Physical and computational domain decompositions for modeling subsurface flows Contemporary Mathematics 218, American Mathematical Society (1998) 217-228.
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    • I. Yotov, Mortar mixed finite element methods on irregular multiblock domains, IMACS Series in Comp. Appl. Math. vol. 4 (1998) 239-244.
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    • T. Arbogast, C. N. Dawson, P. T. Keenan, M. F. Wheeler, and I. Yotov, Enhanced cell-centered finite differences for elliptic equations on general geometry, SIAM J. Sci. Comp. 19:2 (1998) 404-425.
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    • I. Yotov, A mixed finite element discretization on non-matching multiblock grids for a degenerate parabolic equation arising in porous media flow, East-West J. Numer. Math. 5 (1997) 211-230.
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    • T. Arbogast, M. F. Wheeler, and I. Yotov, Mixed finite elements for elliptic problems with tensor coefficients as cell-centered finite differences, SIAM J. Numer. Anal. 34:2 (1997) 828-852.
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    • T. Arbogast and I. Yotov, A non-mortar mixed finite element method for elliptic problems on non-matching multiblock grids, Comp. Meth. in Appl. Mech. and Engng. 149 (1997) 255-265.
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    • Selected Presentations

    Parallel multiblock reservoir simulation