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2006
M. Hanslien, K. H. Karlsen and A. Tveito. "On a Finite Difference Scheme for a Beeler-Reuter Based Model of Cardiac Electrical Activity." International Journal of Numerical Analysis and Modeling 3 (2006): 395-412.
2005
M. Hanslien, K. H. Karlsen and A. Tveito. "A Maximum Principle for an Explicit Finite Difference Scheme Approximating the Hodgkin-Huxley Model." BIT 45 (2005): 725-741.
M. Bendahmane and K. H. Karlsen. "Renormalized Solutions of an Anisotropic Reaction-Diffusion-Advection System With L^1 Data Modeling the Propagation of an Epidemic Disease." Communications on Pure and Applied Analysis 5 (2005): 733-762.
2001
V. Haugse, K. H. Karlsen, K. Lie and J. R. Natvig. "Numerical Solution of the Polymer System by Front Tracking." Transp. Porous Media 44 (2001): 63-83.
H. Holden, K. H. Karlsen, K. Lie and N. H. Risebro. Operator Splitting for Convection-Dominated Nonlinear Partial Differential Equations In Godunov Methods:Theory and Applications, Edited by E. F. Toro., 2001.
K. H. Karlsen, K. 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. 173 (2001): 636-663.
2000
K. H. Karlsen, K. Lie and N. H. Risebro. "A Fast Marching Method for Reservoir Simulation." Comput. Geosci. 4 (2000): 185-206,.
S. Evje, K. H. Karlsen, K. Lie and N. H. Risebro. "Front Tracking and Operator Splitting for Nonlinear Degenerate Convection-Diffusion Equations." In Parallel solution of partial differential equations, edited by P. Bjørstad and M. Luskin, 209-227,. IMA Vol. Math. Appl. Springer, 2000.
R. Bürger, S. Evje, K. H. Karlsen and K. Lie. "Numerical Methods for the Simulation of the Settling of Flocculated Suspensions." Chem. Eng. J. 80 (2000): 91-104,.
H. Holden, K. H. Karlsen and K. Lie. "Operator Splitting Methods for Degenerate Convection-Diffusion Equations I: Convergence and Entropy Estimates." CMS Conference Proceedings 129 (2000).
H. Holden, K. H. Karlsen and K. Lie. "Operator Splitting Methods for Degenerate Convection-Diffusion Equations II: Numerical Examples With Emphasis on Reservoir Simulation." Comput. Geosci. 4 (2000): 287-322,.
1999
K. H. Karlsen, K. Lie and N. H. Risebro. A Front Tracking Method for Conservation Laws With Boundaryconditions In Hyperbolic problems: theory, numerics, applications (Seventh international conference in Zürich, 1998), Edited by M. Fey and R. Jeltsch. Int. Series of Numerical Mathematics. Birkhäuser, 1999.
K. H. Karlsen and K. Lie. "An Unconditionally Stable Splitting Scheme for a Class of Nonlinear Parabolic Equations." IMA J. Numer. Anal. 19 (1999): 609-636,.
1998
K. H. Karlsen, K. Brusdal, H. K. Dahle, S. Evje and K. Lie. "The Corrected Operator Splitting Approach Applied to an Advection-Diffusion Problem." Comput. Methods Appl. Mech. Engrg 167 (1998): 239-260,.
K. Lie, V. Haugse and K. H. Karlsen. "Dimensional Splitting With Front Tracking and Adaptive Local Grid Refinement." Numer. Methods Partial Differential Equations 14 (1998): 627-648,.
K. H. Karlsen, K. Lie, N. H. Risebro and J. Føyen. "A Front-Tracking Approach to a Two-Phase Fluid-Flow Model With Capillary Forces." In Situ 22 (1998): 59-89,.