In journals | In procedings | Books, book chapters, etc

In Journals

  1. J. Li, L. Zhao, O. Møyner, K.-A. Lie. A new near-wellbore modeling method for deviated wells in corner-point grid. Advances in Geo-Energy Research, 2025, 15(2): 112-128. DOI: 10.46690/ager.2025.02.04.
  2. B. Aslam, B. Yan, K.-A. Lie, S. Krogstad, O. Møyner, and X. He. A novel hybrid physics/data-driven model for fractured reservoir simulation. SPE Journal, 2024. DOI: 10.2118/219110-PA
  3. L. Salo-Salgado, O. Møyner, K.-A. Lie, and R. Juanes. Three-dimensional simulation of geologic carbon dioxide sequestration using MRST. Advances in Geo-Energy Research, 2024. DOI: 10.46690/ager.2024.10.06.
  4. W. Xiong, L.-H. Zhang, Y.-L. Zhao, S.-M. Wen, K. Bao, O. Møyner, and K.-A. Lie. Compositional simulation for carbon storage in porous media using an electrolyte association equation of state. SPE Journal, 2024. DOI: 10.2118/219734-PA.
  5. J M. Nordbotten, M. A. Fernø, B. Flemisch, A. R. Kovscek, and K.-A. Lie. The 11th Society of Petroleum Engineers Comparative Solution Project: Problem definition. SPE Journal, 2024. DOI: 10.2118/218015-PA.
  6. K.-A. Lie and S. Krogstad. Data-driven modelling with coarse-grid network models. Computational Geosciences, 2023. DOI: 10.1007/s10596-023-10237-y.
  7. O. Møyner, A. F. Rasmussen, Ø. Klemetsdal, H. M. Nilsen, A. Moncorgé, and K.-A. Lie. Nonlinear domain-decomposition preconditioning for robust and efficient field-scale simulation of subsurface flow. Computational Geosciences, 2023. DOI: 10.1007/s10596-023-10215-4
  8. K.-A. Lie and S. Krogstad. Comparison of two different types of reduced graph-based reservoir models: Interwell networks (GPSNet) versus aggregated coarse-grid networks (CGNet). Geoenergy Science and Engineering Volume 221, February 2023, 111266. DOI: 10.1016/j.petrol.2022.111266.
  9. G. P. Oliveira, T. N. E. Rodrigues, and K.-A. Lie. GAWPS: A MRST-based module for wellbore profiling and graphical analysis of flow units. Advances in Geo-Energy Research, 2021, 6(1): 38-53. DOI: 10.46690/ager.2022.01.04.
  10. F. Watson, S. Krogstad, and K.-A. Lie. The use of flow diagnostics to rank model ensembles. Computational Geosciences, 2021. In press. DOI: 10.1007/s10596-021-10087-6.
  11. Ø. S. Klemetsdal, A. Moncorgé, H. M. Nilsen, O. Møyner, and K.-A. Lie. An adaptive sequential fully implicit domain-decomposition solver. SPE Journal, 2021. DOI: 10.2118/203991-PA
  12. S. Ma, B. Ju, L. Zhao, K.-A. Lie, Y. Dong, Q. Zhang, and Y. Tian. Embedded discrete fracture modelling: flow diagnostics, non-Darcy flow, and well placement optimization. Journal of Petroleum Science and Engineering, Vol. 208, Part C, January 2022, 109477. DOI: 10.1016/j.petrol.2021.109477. Springer Share Link.
  13. Ø. S. Klemetsdal, A. Moncorgé, O. Møyner, and K-A. Lie. A numerical study of the additive Schwarz preconditioned exact Newton method (ASPEN) as a nonlinear preconditioner for immiscible and compositional porous media flow. Computational Geosciences, 2021. DOI: 10.1007/s10596-021-10090-x
  14. Ø. S. Klemetsdal, O. Møyner, A. Moncorgé, H. M. Nilsen, and K.-A. Lie. High-resolution compositional reservoir simulation with dynamic coarsening and local timestepping for unstructured grids. SPE Journal, Vol. 26, Issue 06, pp. 4157-4173, 2021. DOI: 10.2118/203982-PA
  15. X. Raynaud, A. Pizzolato, A. Johansson, F. Caresani, A. Ferrari, O. Møyner, H. M. Nilsen, A. Cominelli, and K.-A. Lie. Toward accurate reservoir simulations on unstructured grids: design of simple error estimators and critical benchmarking of consistent discretization methods for practical implementation. SPE Journal, , Vol. 26, Issue 06, pp. 4109-4127,2021. DOI: 10.2118/203920-PA.
  16. A. F. Rasmussen, T. H. Sandve, K. Bao, A. Lauser, J. Hove, B. Skaflestad, R. Klöfkorn, M. Blatt, A. B. Rustad, O. Sævareid, K.-A. Lie, A. Thune. The Open Porous Media Flow Reservoir Simulator. Computers and Mathematics with Applications, Vol. 81, pp. 159-185, 2021. DOI: 10.1016/j.camwa.2020.05.014.
  17. Ø. S. Klemetsdal and K.-A. Lie. Dynamic coarsening and local reordered nonlinear solvers for simulating transport in porous media. SPE Journal. Vol. 25, No. 4, pp. 2021-2040, 2021. DOI: 10.2118/201089-PA.
  18. G. Linga, O. Møyner, H.M. Nilsen, A. Moncorgé, and K.-A. Lie. An implicit local time-stepping method based on cell reordering for multiphase flow in porous media. Journal of Computational Physics: X, Vol. 6, March 2020, 100051. DOI: 10.1016/j.jcpx.2020.100051
  19. Ø. S. Klemetsdal, A. F. Rasmussen, O. Møyner, and K.-A. Lie. Efficient reordered nonlinear Gauss-Seidel solvers with higher order for black-oil models. Comput. Geosci., Vol. 24, pp. 593-607, 2020. DOI: 10.1007/s10596-019-09844-5, Springer Nature SharedIt
  20. K.-A. Lie, T. S. Mykkeltvedt, and O. Møyner. A fully implicit WENO scheme on stratigraphic and unstructured polyhedral grids. Comput. Geosci., Vol. 24, pp. 405-423, 2020. DOI: 10.1007/s10596-019-9829-x, Springer Nature SharedIt
  21. Ø. S. Klemetsdal, O. Møyner, and K.-A. Lie. Accelerating multiscale simulation of complex geomodels by use of dynamically adapted basis functions. Comput. Geosci., Vol. 24, pp. 459-476, 2020. DOI: 10.1007/s10596-019-9827-z, Springer Nature SharedIt
  22. Ø. S. Klemetsdal, O. Møyner, and K.-A. Lie. Robust nonlinear Newton solver with adaptive interface-localized trust regions. SPE Journal, Vol. 24, Issue 04, pp. 1576-1594, 2019. DOI: 10.2118/195682-PA
  23. H. A. Marefat, M. A. Ashjari Aghdam, and K.-A. Lie. Preserving vorticity improves the accuracy of multiscale solvers. J. Petrol. Sci. Eng., Vol. 182, 2019, 106231. DOI: 10.1016/j.petrol.2019.106231
  24. R. L. Berge, Ø. S. Klemetsdal, and K.-A. Lie. Unstructured Voronoi grids conforming to lower-dimensional objects. Comput. Geosci., Vol. 23, Issue 1, pp 169-188 2019. DOI: 10.1007/s10596-018-9790-0. Springer Nature SharedIt
  25. M. G. Zefreh, H. M. Nilsen, K.-A. Lie, X. Raynaud, and F. Doster. Streamline simulation of a reactive advective flow with discontinuous flux function. Comput. Geosci., Volume 23, Issue 2, pp 255-271, 2019. DOI: 10.1007/s10596-018-9771-3.
  26. R. Allen, H. M. Nilsen, K.-A. Lie, O. Møyner, and O. Andersen. Using simplified methods to explore the impact of parameter uncertainty on CO2 storage estimates with application to the Norwegian Continental Shelf. International Journal of Greenhouse Gas Control, Vol. 75, pp. 198-213, 2018. DOI: 10.1016/j.ijggc.2018.05.017
  27. R. Allen, H. M. Nilsen, O. Andersen, and K.-A. Lie. Ranking and categorizing large-scale saline aquifer formations based on optimized CO2 storage potentials and economic factors. International Journal of Greenhouse Gas Control, Vol. 65, pp. 182-194, 2017. DOI: 10.1016/j.ijggc.2017.07.023
  28. K.-A. Lie, O. Møyner, and J. R. Natvig. Use of multiple multiscale operators to accelerate simulation of complex geomodels. SPE Journal, Vol. 22, Issue 6, pp. 1929-1945, 2017. DOI: 10.2118/182701-PA
  29. H. M. Nilsen, S. Krogstad, O. Andersen, R. Allen, K.-A. Lie. Using sensitivities and vertical-equilibrium models for parameter estimation of CO2 injection models with application to the Sleipner injection to measured data. Energy Procedia, Vol. 114, pp. 3476-3495, 2017. DOI: 10.1016/j.egypro.2017.03.1478
  30. R. Allen, H. M. Nilsen, O. Andersen, K.-A. Lie. Categorization of Norwegian Continental Shelf formations in terms of geological CO2 storage potentials. Energy Procedia, Vol. 114, pp. 4583-4594, 2017. DOI: 10.1016/j.egypro.2017.03.1579
    Revised version in which we have corrected inaccuracies in the calculation of pressure values that determine whether an aquifer is constrained by leakage or pressure buildup
  31. T. S. Mykkeltvedt, X. Raynaud, and K.-A. Lie. Fully implicit higher-order schemes applied to polymer flooding. Comput. Geosci., Vol. 21, Issue 5-6, pp. 1245-1266, 2017. DOI: 10.1007/s10596-017-9676-6. Springer Nature SharedIt
  32. S. Krogstad, K.-A. Lie, H. M. Nilsen, C. F. Berg, and V. Kippe. Efficient flow diagnostics proxies for polymer flooding. Comput. Geosci., Vol. 21, Issue 5-6, pp. 1203-1218, 2017. DOI: 10.1007/s10596-017-9681-9
  33. R. Allen, H. M. Nilsen, O. Andersen, and K.-A. Lie. On obtaining optimal well rates and placement for CO2 storage. Comput. Geosci., Vol. 21, Issue 5-6, pp. 1403-1422, 2017. DOI: 10.1007/s10596-017-9631-6. Springer Nature SharedIt
  34. K.-A. Lie, O. Møyner, J. R. Natvig, A. Kozlova, K. Bratvedt, S. Watanabe, and Z. Li. Successful application of multiscale methods in a real reservoir simulator environment. Comput. Geosci., Vol. 21, Issue 5-6, pp. 981-998, 2017. DOI: 10.1007/s10596-017-9627-2
  35. K. Bao, K.-A. Lie, O. Møyner, and M. Liu. Fully implicit simulation of polymer flooding with MRST. Comput. Geosci., Vol. 21, Issue 5-6, pp. 1219-1244, 2017. DOI: 10.1007/s10596-017-9624-5. Springer Nature SharedIt
  36. O. Møyner and K.-A. Lie. A multiscale restriction-smoothed basis method for compressible black-oil models. SPE Journal, Vol. 21, No. 06, pp. 2079-2096, 2016. DOI: 10.2118/173265-PA
  37. S. Shah, O. Møyner, M. Tene, K.-A. Lie, and H. Hajibeygi. The multiscale restriction smoothed basis method for fractured porous media (F-MsRSB). J. Comput. Phys., Vol. 318, pp. 36-57, 2016. DOI: 10.1016/j.jcp.2016.05.001
  38. S. T. Hilden, O. Møyner, K.-A. Lie, and K. Bao. Multiscale simulation of polymer flooding with shear effects. Transport in Porous Media, Vol. 113, Issue 1, pp. 111-135, 2016. DOI: 10.1007/s11242-016-0682-2
  39. X. Raynaud, K.-A. Lie, H. M. Nilsen, and A. Rasmussen. The single-cell transport problem for two-phase flow with polymer. Comput. Geosci., Vol. 20, Issue 3, pp. 495-507, 2016. DOI: 10.1007/s10596-015-9502-y Springer Nature SharedIt
  40. K.-A. Lie, H. M. Nilsen, O. Andersen, and O. Møyner. A simulation workflow for large-scale CO2 storage in the Norwegian North Sea. Comput. Geosci., Vol. 20, Issue 3, pp. 607-622, 2016. DOI: 10.1007/s10596-015-9487-6 Springer Nature SharedIt
  41. H. M. Nilsen, K.-A. Lie, and O. Andersen. Robust simulation of sharp-interface models for fast estimation of CO2 trapping capacity in large-scale aquifer systems. Comput. Geosci., Vol. 20, Issue 1, pp. 93-113, 2016. DOI: 10.1007/s10596-015-9549-9
  42. H. M. Nilsen, K.-A. Lie, and O. Andersen. Fully-implicit simulation of vertical-equilibrium models with hysteresis and capillary fringe. Comput. Geosci., Vol. 20, Issue 1, pp. 49-67, 2016. DOI: 10.1007/s10596-015-9547-y
  43. O. Andersen, K.-A. Lie, and H. M. Nilsen. An open-source toolchain for simulation and optimization of aquifer-wide CO2 storage. Energy Procedia, Vol. 86, pp. 324-333, 2016. DOI: 10.1016/j.egypro.2016.01.033
  44. O. Møyner and K.-A. Lie. A multiscale restriction-smoothed basis method for high contrast porous media represented on unstructured grids. J. Comput. Phys, Vol. 304, pp. 46-71, 2016. DOI: 10.1016/j.jcp.2015.10.010
  45. H. M. Nilsen, K.-A. Lie, and O. Andersen. Analysis of CO2 trapping capacities and long-term migration for geological formations in the Norwegian North Sea using MRST-co2lab. Computers & Geoscience, Vol. 79, pp. 15-26, 2015. DOI: 10.1016/j.cageo.2015.03.001
  46. H. M. Nilsen, K.-A. Lie, O. Møyner, and O. Andersen. Spill-point analysis and structural trapping capacity in saline aquifers using MRST-co2lab. Computers & Geoscience, Vol. 75, pp. 33-43, 2015. DOI: 10.1016/j.cageo.2014.11.002
  47. M. Pal, S. Lamine, K.-A. Lie, and S. Krogstad. Validation of the multiscale mixed finite-element method. Int. J. Numer. Meth. Fluids, Vol. 77, Issue 4, pp. 206-223, 2015. DOI: 10.1002/fld.3978
  48. S. Kaulmann, B. Flemisch, B. Haasdonk, K.-A. Lie, and M. Ohlberger. The localized reduced basis multiscale method for two-phase flows in porous media. Int. J. Numer. Meth. Engng., Vol. 102, No. 5, pp. 1018-1040, 2015. DOI: 10.1002/nme.4773
  49. M. L. Sætra, A. R. Brodtkorb, and K.-A. Lie. Efficient GPU-implementation of adaptive mesh refinement for the shallow-water equations. J. Sci. Comp., Vol. 63, No. 1, pp. 23-48, 2015. DOI: 10.1007/s10915-014-9883-4
  50. O. Møyner, S. Krogstad, and K.-A. Lie. The application of flow diagnostics for reservoir management. SPE J., Vol. 20, No. 2, pp. 306-323, 2015. DOI: 10.2118/171557-PA
  51. K.-A. Lie, H. M. Nilsen, A. F. Rasmussen, and X. Raynaud. Fast simulation of polymer injection in heavy-oil reservoirs based on topological sorting and sequential splitting. SPE J., Vol. 19, No. 6, pp. 991-1004, 2014. DOI: 10.2118/163599-PA.
  1. O. Møyner and K.-A. Lie. The multiscale finite-volume method on stratigraphic grids. SPE J., Vol. 19, No. 5, pp. 816-831, 2014. DOI: 10.2118/163649-PA.
  2. O. Møyner and K.-A. Lie. A multiscale two-point flux-approximation method. J. Comput. Phys., Vol. 275, pp. 273-293, 2014. DOI: 10.1016/j.jcp.2014.07.003.
  3. K.-A. Lie, J. R. Natvig, S. Krogstad, Y. Yang, and X.-H. Wu. Grid adaptation for the Dirichlet-Neumann representation method and the multiscale mixed finite-element method. Comput. Geosci., Vol. 18, No. 3, pp. 357-372, 2014. DOI: 10.1007/s10596-013-9397-4
  4. F. O. Alpak, M. Pal, and K.-A. Lie. A multiscale method for modeling flow in stratigraphically complex reservoirs. SPE J., Vol. 17, No. 4, pp. 1056-1070, 2012. DOI: 10.2118/140403-PA
  5. H. M. Nilsen, A. R. Syversveen, K.-A. Lie, J. Tveranger, and J. M. Nordbotten. Impact of top-surface morphology on CO2 storage capacity. Int. J. Greenhouse Gas Control, Vol. 11, pp. 221-235, 2012. DOI: 10.1016/j.ijggc.2012.08.012
  6. H. M. Nilsen, K.-A. Lie, and J. R. Natvig. Accurate modelling of faults by multipoint, mimetic, and mixed methods. SPE J., Vol. 17, No. 2, pp. 568-579, June 2012. DOI: 10.2118/149690-PA.
  7. 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.
  8. 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
  9. 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.
  10. 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: 10.2018/119132-PA
  11. M. Krotkiewski, 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, 2011. DOI: 10.4208/cicp.290610.020211a
  12. H. M. Nilsen, P. A. Herrera, M. Ashraf, I. S. Ligaarden, M. Iding, C. Hermanrud, K.-A. Lie, J. M. Nordbotten, H. K. Dahle, and E. Keilegavlen. Field-case simulation of CO2-plume migration using vertical-equilibrium models. Energi Procedia, Vol. 4, pp. 3801-3808, 2011. DOI: 10.1016/j.egypro.2011.02.315
  13. A. R. Brodtkorb, T. R. Hagen, K.-A. Lie, and J. R. Natvig. Simulation and visualization of the Saint-Venant system using GPUs. Comput. Visual. Sci. (Special issue on Hot Topics in Computational Engineering), Vol. 13, No. 7, pp. 341--353, 2010. DOI: 10.1007/s00791-010-0149-x
  14. 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
  15. B. Eikemo, K.-A. Lie, G.T. Eigestad, and H.K. Dahle. Discontinuous Galerkin methods for advective transport in single-continuum models of fractured media. Adv. Water Resour. Vol. 32, Issue 4, pp. 493-506. 2009. DOI: 10.1016/j.advwatres.2008.12.010.
  16. 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
  17. 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, Vol. 227, Issue 24, pp. 10108-10124, 2008. doi:10.1016/j.jcp.2008.08.024.
  18. 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, pp. 99--111, March 2008. DOI: 10.2118/106228-PA
  19. V. Kippe, J. E. Aarnes, and K.-A. Lie. A comparison of multiscale methods for elliptic problems in porous media flow. Comput. Geosci., Special issue on multiscale methods. Vol. 12, No. 3, pp. 377-398, 2008. DOI: 10.1007/s10596-007-9074-6
  20. J. E. Aarnes, S. Krogstad, and K.-A. Lie. Multiscale mixed/mimetic methods on corner-point grids. Comput. Geosci., Special issue on multiscale methods. Vol. 12, No. 3, pp. 297-315, 2008. DOI: 10.1007/s10596-007-9072-8
  21. R. Juanes and K.-A. Lie. Numerical modeling of multiphase first-contact miscible flows. Part 2. Front-tracking and streamline simulation. Transp. Porous Media, Vol. 72, No. 1/March, pp. 97-120, 2008. DOI: 10.1007/s11242-007-9139-y
  22. J. R. Natvig, K.-A. Lie, B. Eikemo, and I. Berre. An efficient discontinuous Galerkin method for advective transport in porous media. Adv. Water Resour, Vol. 30, Issue 12, pp. 2424-2438, 2007. DOI: 10.1016/j.advwatres.2007.05.015
  23. 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. Adv. Water Resour. Vol. 30, Issue 4, pp. 1027-1045, 2007. DOI: 10.1016/j.advwatres.2006.09.00.
  24. R. Juanes and K.-A. Lie. Numerical modeling of multiphase first-contact miscible flows. Part 1. Analytical Riemann solver. Transp. Porous Media, Vol. 67, No. 3 / April, pp. 375-393, 2007. DOI: 10.1007/s11242-006-9031-1.
  25. V. R. Stenerud and K.-A. Lie. A multiscale streamline method for inversion of production data. J. Pet. Sci. Eng., Vol. 54, pp. 79-92, 2006. DOI: 10.1016/j.petrol.2006.08.003.
  26. 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 Model. Simul., Vol. 5, No. 2, pp. 337-363, 2006. DOI: 10.1137/050634566
  27. I. Berre, K. H. Karlsen, K.-A. Lie, and J. R. Natvig. Fast computation of arrival times in heterogeneous media. Comput. Geosci., Vol. 9, No. 4, pp. 179-201, 2005. DOI 10.1007/s10596-005-9002-6
  28. T. R. Hagen, J. M. Hjelmervik, K.-A. Lie, J. R. Natvig, M. Ofstad Henriksen. Visual simulation of shallow-water waves. Simul. Model. Pract. Theory, Vol. 13, Issue 8 (Special Issue on Programmable Graphics Hardware), pp.716-726, November 2005. DOI: 10.1016/j.simpat.2005.08.006
  29. K.-A. Lie and R. Juanes. A front-tracking method for the simulation of three-phase flow in porous media. Comput. Geosci., Vol. 9, No. 1, pp. 29-59, March 2005. DOI: 10.1007/s10596-005-5663-4
  30. J. E. Aarnes, V. Kippe, and K.-A. Lie. Mixed multiscale finite elements and streamline methods for reservoir simulation of large geomodels. Adv. Water Resour., Vol. 28, Issue 3, pp. 257-271, 2005. DOI: 10.1016/j.advwatres.2004.10.007
  31. K.-A. Lie and S. Noelle. On the artificial compression method for second-order nonoscillatory central difference schemes for systems of conservation laws. SIAM J. Sci. Comp., Vol. 24, No. 4, pp. 1157-1174, 2003. DOI: 10.1137/S1064827501392880
  32. K.-A. Lie and S. Noelle. An improved quadrature rule for the flux-computation in staggered central difference schemes in multidimensions. J. Sci. Comp., Vol. 18, No. 1, pp. 69-81, February 2003. DOI: 10.1023/A:1020386111898
  33. K. Hvistendahl Karlsen, K.-A. Lie, J. R. Natvig, H. F. Nordhaug, and H. K. Dahle. Operator splitting methods for systems of convection-diffusion equations: nonlinear error mechanisms and correction strategies. J. Comput. Phys., Vol. 173, Issue 2, pp. 636-663, 2001. DOI: 10.1006/jcph.2001.6901
  34. V. Haugse, K. H. Karlsen, K.-A. Lie, and J. R. Natvig. Numerical solution of the polymer system by front tracking. Transp. Porous Media, Vol 44, No 1, pp. 63-83, 2001. DOI: 10.1023/A:1010740024800
  35. H. Holden, K. Hvistendahl Karlsen, and K.-A. Lie. Operator splitting methods for degenerate convection-diffusion equations II: numerical examples with emphasis on reservoir simulation and sedimentation. Comput. Geosci., Vol. 4, No. 4, pp. 287-322, 2000. DOI: 10.1023/A:1011582819188
  36. H. Holden, K. Hvistendahl Karlsen, and K.-A. Lie. Operator splitting methods for degenerate convection-diffusion equations I: convergence and entropy estimates. CMS Conf. Proc., Vol. 129, pp. 293-316, 2000.
  37. K. Hvistendahl Karlsen, K.-A. Lie, and N. H. Risebro. A fast marching method for reservoir simulation. Comput. Geosci., Vol. 4, No. 2, pp. 185-206, 2000. DOI: 10.1023/A:1011564017218
  38. K.-A. Lie. Front tracking for one-dimensional quasilinear hyperbolic equations with variable coefficients. Numer. Algorithms, Vol. 24, No. 3, pp. 275-298, 2000.
  39. R. Bürger, S. Evje, K. Hvistendahl Karlsen, and K.-A. Lie. Numerical methods for the simulation of the settling of flocculated suspensions. Chem. Eng. J., Vol. 80, pp. 91-104, 2000.
  40. S. Evje, K. Hvistendahl Karlsen, K.-A. Lie, and N. H. Risebro. Front tracking and operator splitting for nonlinear degenerate convection-diffusion equations. In "Parallel solution of partial differential equations", Eds., P. Bjørstad and M. Luskin, IMA Vol. Math. Appl., Vol. 120, pp. 209-227, Springer Verlag, 2000.
  41. K.-A. Lie. A dimensional splitting method for quasilinear hyperbolic equations with variable coefficients. BIT, Vol. 39, No. 4, pp. 683-700, 1999. Awarded the Carl-Erik Fröberg Prize for young nordic authors.
  42. R. Holdahl, H. Holden, and K.-A. Lie. Unconditionally stable splitting methods for the shallow water equations. BIT, Vol. 39, No. 3, pp. 451-472, 1999.
  43. K. Hvistendahl Karlsen and K.-A. Lie. An unconditionally stable splitting scheme for a class of nonlinear parabolic equations. IMA J. Num. Anal., Vol. 19, No. 4, pp. 609-635, 1999.
  44. H. Holden, K.-A. Lie, and N. H. Risebro. An unconditionally stable method for the Euler equations. J. Comput. Phys. Vol. 150, no. 1, pp. 76-96, 1999.
  45. K. Hvistendahl Karlsen, K.-A. Lie, N. H. Risebro, and J. Frøyen. A front-tracking approach to a two-phase fluid-flow model with capillary forces. In Situ (A Special Issue on Reservoir Simulation), Vol. 22, Issue No. 1, pp. 59-89, 1998.
  46. K. Hvistendahl Karlsen, K. Brusdal, H. K. Dahle, S. Evje, and K.-A. Lie. The corrected operator splitting approach applied to an advection-diffusion problem. Comput. Methods Appl. Mech. Engrg., Vol. 167, Issue 3-4, pp. 239-260, 1998.
  47. K.-A. Lie, V. Haugse, and K. Hvistendahl Karlsen. Dimensional splitting with front tracking and adaptive local grid refinement. Numer. Methods Partial Differential Equations, Vol. 14, No. 5, pp. 627-648, 1998.