Showing papers by "Steinar Evje published in 1999"

Viscous splitting approximation of mixed hyperbolic-parabolic convection-diffusion equations

Abstract: We first analyse a semi-discrete operator splitting method for nonlinear, possibly strongly degenerate, convection-diffusion equations Due to strong degeneracy, solutions can be discontinuous and are in general not uniquely determined by their data Hence weak solutions satisfying an entropy condition are sought We then propose and analyse a fully discrete splitting method which employs a front tracking scheme for the convection step and a finite difference scheme for the diffusion step Numerical examples are presented which demonstrate that our method can be used to compute physically correct solutions to mixed hyperbolic-parabolic convection-diffusion equations

Degenerate Convection-Diffusion Equations and Implicit Monotone Difference Schemes

Abstract: We analyse implicit monotone finite difference schemes for nonlinear, possibly strongly degenerate, convection-diffusion equations in one spatial dimension. Since we allow strong degeneracy, solutions can be discontinuous and are in general not uniquely determined by their data. We thus choose to work with weak solutions that belong to the BV (in space and time) class and, in addition, satisfy an entropy condition. The difference schemes are shown to converge to the unique BV entropy weak solution of the problem. This paper complements our previous work [8] on explicit monotone schemes.