In press

1. F. O. Alpak, M. Pal, and K.-A. Lie. A multiscale method for modeling flow in stratigraphically complex reservoirs. SPE J., to appear.
2. H. M. Nilsen, K.-A. Lie, and J. R. Natvig. Accurate modelling of faults by multipoint, mimetic, and mixed methods. SPE J., to appear, DOI: 10.2118/149690-PA.

2012

1. K.-A. Lie, J. R. Natvig, and H. M. Nilsen. Discussion of dynamics and operator splitting techniques for two-phase flow with gravity. Int. J Numer. Anal. Mod. (Special issue in memory of Magne Espedal), Vol. 9, No. 3, pp. 684-700, 2012.
2. R. A. Klausen, A. F. Rasmussen, and A. F. Stephansen. Velocity interpolation and streamline tracing on irregular geometries. Comput. Geosci., Vol. 16, No. 2, pp. 261-276, 2012. DOI: 10.1007/s10596-011-9256-0.
3. K.-A. Lie, S. Krogstad, I. S. Ligaarden, J. R. Natvig, H. M. Nilsen, and B. Skaflestad. Open source MATLAB implementation of consistent discretisations on complex grids. Comput. Geosci., Vol. 16, No. 2, pp. 297-322, 2012. DOI: 10.1007/s10596-011-9244-4.
4. V. L. Hauge, K.-A. Lie, and J. R. Natvig. Flow-based coarsening for multiscale simulation of transport in porous media. Comput. Geosci.,  Vol. 16, No. 2, pp. 391-408, 2012. DOI: 10.1007/s10596-011-9230-x

2011

1. J. R. Natvig, B. Skaflestad, F. Bratvedt, K. Bratvedt, K.-A. Lie, V. Laptev, and S. K. Khataniar. Multiscale mimetic solvers for efficient streamline simulation of fractured reservoirs. SPE J., Vol. 16, No. 4, pp. 880-880, 2011. DOI: 10.2118/119132-PA.
2. M. Krokiewski, I. Ligaarden, K.-A. Lie, D. W. Schmid. On the importance of the Stokes-Brinkman equations for computing effective permeability in carbonate karst reservoirs.Comm. Comput. Phys, Vol. 10, No. 5, pp. 1315-1332. DOI: 10.4208/cicp.290610.020211a
3. S. Krogstad, V. L. Hauge, and A. F. Gulbransen. Adjoint multiscale mixed finite elements. SPE J., Vol. 16, No. 1, pp. 162-171, 2011. DOI: 10.2118/119112-PA.

2010

1. A. F. Gulbransen, V. L. Hauge, and K.-A. Lie. A multiscale mixed finite-element method for vuggy and naturally-fractured reservoirs. SPE J., Vol. 15, No. 12, pp. 395-403, 2010.  DOI: 10.2118/119104-PA.

2009

1. S. Krogstad and L. J. Durlofsky. Multiscale mixed-finite-element modeling of coupled wellbore/near-well flow. SPE J., Vol. 14, No. 1, pp. 78-87, March 2009. DOI: 10.2118/106179-PA.
2. B. Eikemo, K.-A. Lie, H.K. Dahle, and G.T. Eigestad.  A discontinuous Galerkin method for transport in fractured media using unstructured triangular grids. Adv. Water Resour., Vol. 32, Issue 4, April 2009, pp. 493-506, DOI: 10.1016/j.advwatres.2008.12.010.
3. V. R. Stenerud, K.-A. Lie, and V. Kippe. Generalized travel-time inversion on unstructured grids. J. Pet. Sci. Eng. Vol. 65, Issues 3-4, pp. 175-187, 2009. DOI: 10.1016/j.petrol.2008.12.030.
4. V. L. Hauge and J. E. Aarnes. Modeling of fractured two-phase flow in fractured porous media on unstructured non-uniform coarse grids. Transport in Porous Media, Vol. 77, No. 3 / April, pp. 373-398, 2009. DOI: 10.1007/s11242-008-9284-y.

2008

1. J. R. Natvig and K.-A. Lie. Fast computation of multiphase flow in porous media by implicit discontinuous Galerkin schemes with optimal ordering of elements. J. Comput. Phys, Volume 227, Issue 24, pp. 10108-10124, 2008. DOI: 10.1016/j.jcp.2008.08.024.
2. J.E. Aarnes and Y. Efendiev. Mixed multiscale finite element for stochastic porous media flows.  SIAM J. Sci. Comp., Volume 30, Issue 5, pp. 2319-2339, 2008. DOI: 10.1137/07070108X.
3. V. Kippe, J. E. Aarnes, and K.-A. Lie. A comparison of multiscale methods for elliptic problems in porous media flow. Computational Geosciences, Vol. 12, No. 3, pp. 377-398, 2008. DOI: 10.1007/s10596-007-9074-6
4. J. E. Aarnes, S. Krogstad, and K.-A. Lie. Multiscale mixed/mimetic methods on corner-point grids. Computational Geosciences, Vol. 12, No. 3, pp. 297-315, 2008.  DOI: 10.1007/s10596-007-9072-8
5. J. E. Aarnes, Y. Efendiev, and L. Jiang. Mixed multiscale finite element methods using limited global information. Multiscale Modelling and Simulation, Volume 7, Issue 2, pp. 655-676, 2008. DOI: 10.1137/070688481
6. J.E. Aarnes and Y. Efendiev. A multiscale method for modeling transport in porous media on unstructured corner-point grids. Journal of Algorithms and Computational Technology, Volume 2, Number 2, pp. 299-318, 2008. DOI: 10.1260/174830108784646616
7. V. R. Stenerud, V. Kippe, K.-A. Lie, and A. Datta-Gupta. Adaptive multiscale streamline simulation and inversion for high-resolution geomodels.  SPE J., Vol. 13, No. 1/March, pp. 99--111, 2008. DOI: 10.2118/106228-PA.
8. R. Juanes and K.-A. Lie. Numerical modeling of multiphase first-contact miscible flows. Part 2. Front-tracking and streamline simulation. Transport in Porous Media, Vol. 72, No. 1/March, pp. 97-120, 2008.  DOI: 10.1007/s11242-007-9139-y

2007

1. J. R. Natvig, K.-A. Lie, B. Eikemo, and I. Berre. An efficient discontinous Galerkin method for advective transport in porous media. Advances in Water Resources, Vol. 30, Issue 12, December 2007, pp. 2424-2438. DOI: 10.1016/j.advwatres.2007.05.015
2. J. E. Aarnes, V. L. Hauge, and Y. Efendiev. Coarsening of three-dimensional structured and unstructured grids for subsurface flow. Advances in Water Resources, Vol. 30, Issue 11, November 2007, pp. 2177-2193. DOI: 10.1016/j.advwatres.2007.04.007
3. R. Juanes and K.-A. Lie. Numerical modeling of multiphase first-contact miscible flows. Part 1. Analytical Riemann solver. Transport in Porous Media, Vol. 67, No. 3 / April, pp. 375-393, 2007. DOI: 10.1007/s11242-006-9031-1.
4. H. Hægland, H. K. Dahle, G. T. Eigestad, K.-A. Lie, and I. Aavatsmark. Improved streamlines and time-of-flight for streamline simulation on irregular grids. Advances in Water Resources, Volume 30, Issue 4, pp. 1027-1045, 2007. DOI: 10.1016/j.advwatres.2006.09.002.

2004-2006

1. J. E. Aarnes and Y. Efendiev. An adaptive multiscale method for simulation of fluid flow in heterogeneous porous media. Multiscale Modelling and Simulation, Vol. 5, No. 3, pp. 918-939, 2006. DOI: 10.1137/050645117.
2. J. E. Aarnes, S. Krogstad, and K.-A. Lie. A hierarchical multiscale method for two-phase flow based upon mixed finite elements and nonuniform coarse grids, Multiscale Modelling and Simulation, Vol. 5, No. 2, pp. 337-363, 2006. DOI: 10.1137/050634566.
3. K.-A. Lie and R. Juanes. A front-tracking method for the simulation of three-phase flow in porous media. Computational Geosciences, Vol. 9, No. 1, pp. 29-59, March 2005. DOI: 10.1007/s10596-005-5663-4.
4. J. E. Aarnes, V. Kippe, and K.-A. Lie. Mixed multiscale finite elements and streamline methods for reservoir simulation of large geomodels. Advances in Water Resources, Vol. 28, Issue 3, pp. 257-271, 2005. DOI: 10.1016/j.advwatres.2004.10.007
5. J. E. Aarnes. Efficient domain decomposition methods for elliptic problems arising from flows in heterogeneous porous media. Comp. Vis. Science, 2005. DOI: 10.1007/s00791-005-0155-6.
6. J. E. Aarnes. On the use of a mixed multiscale finite element method for greater flexibility and increased speed or improved accuracy in reservoir simulation. Multiscale Modelling and Simulation, Vol. 2, No. 3, pp. 421 - 439, 2004. DOI: 10.1137/030600655.