# Knut-Andreas Lie

External collaborator

## Publications

Simula-affiliated publications listed

### 2009

#### Edited books

X. Tai, K. Mørken, O. M. Lysaker and K. Lie

Scale Space and Variational Methods in Computer Vision

### 2004

#### Technical reports

K. Lie and A. Tveito

Development of a Staggered Central Difference Scheme That Does Not Use a Spatial Reconstruction

### 2003

#### Journal Articles

K. Lie and S. Noelle

An Improved Quadrature Rule for the Flux-Computation in Staggered Central Difference Schemes in Multidimensions

J. Sci. Comput.

K. Lie and S. Noelle

On the Artificial Compression Method for Second-Order Nonoscillatory Central Difference Schemes for Systems of Conservation Laws

SIAM J. Sci. Comput.

### 2002

#### Proceedings, refereed

K. Lie and S. Noelle

High Resolution Nonoscillatory Central Difference Schemes for the 2D Euler Equations Via Artificial Compression

Progress in Industrial Mathematics at ECMI 2000

K. Lie, S. Noelle and W. Rosenbaum

On the Resolution and Stability of Central Difference Schemes

Proceedings of the Third International Symposium on: FINITE VOLUMES FOR COMPLEX APPLICATIONS - PROBLEMS AND PERSPECTIVES, Porquerolles

### 2001

#### Journal Articles

V. Haugse, K. H. Karlsen, K. Lie and J. R. Natvig

Numerical Solution of the Polymer System by Front Tracking

Transp. Porous Media

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.

#### Proceedings, refereed

H. Holden, K. H. Karlsen, K. Lie and N. H. Risebro

Operator Splitting for Convection-Dominated Nonlinear Partial Differential Equations

Godunov Methods:Theory and Applications

### 2000

#### Journal Articles

K. H. Karlsen, K. Lie and N. H. Risebro

A Fast Marching Method for Reservoir Simulation

Comput. Geosci.

K. Lie

Front Tracking for One-Dimensional Quasilinear Hyperbolic Equations With Variable Coefficients

Numerical Algorithms

R. Bürger, S. Evje, K. H. Karlsen and K. Lie

Numerical Methods for the Simulation of the Settling of Flocculated Suspensions

Chem. Eng. J.

H. Holden, K. H. Karlsen and K. Lie

Operator Splitting Methods for Degenerate Convection-Diffusion Equations I: Convergence and Entropy Estimates

CMS Conference Proceedings

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.

#### Book Chapters

S. Evje, K. H. Karlsen, K. Lie and N. H. Risebro

Front Tracking and Operator Splitting for Nonlinear Degenerate Convection-Diffusion Equations

Parallel solution of partial differential equations

### 1999

#### Journal Articles

K. Lie

A Dimensional Splitting Method for Quasilinear Hyperbolic Equations With Variable Coefficients

BIT

H. Holden, K. Lie and N. H. Risebro

An Unconditionally Stable Method for the Euler Equations

J. Comput. Phys.

K. H. Karlsen and K. Lie

An Unconditionally Stable Splitting Scheme for a Class of Nonlinear Parabolic Equations

IMA J. Numer. Anal.

R. Holdahl, H. Holden and K. Lie

Unconditionally Stable Splitting Methods for the Shallow Water Equations

BIT

#### Proceedings, refereed

K. H. Karlsen, K. Lie and N. H. Risebro

A Front Tracking Method for Conservation Laws With Boundaryconditions

Hyperbolic problems: theory, numerics, applications (Seventh international conference in Zürich, 1998)

### 1998

#### Journal Articles

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

K. Lie, V. Haugse and K. H. Karlsen

Dimensional Splitting With Front Tracking and Adaptive Local Grid Refinement

Numer. Methods Partial Differential Equations

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