We analyze a system of conservation laws in two space dimensions with a stiff relaxation term. A semi-implicit finite difference method approximating the system is studied and an error bound of order script O sign(√Δt) measured in L1 is derived. This error bound is independent of the relaxation time δ > 0. Furthermore, it is proved that the solutions of the system converge towards the solution of an equilibrium model as the relaxation time δ tends to zero, and that the rate of convergence measured in L1 is of order script O sign(δ1/3). Finally, we present some numerical illustrations.
All Science Journal Classification (ASJC) codes
- Computer Networks and Communications
- Computational Mathematics
- Applied Mathematics