Transient \(L^1\) error estimates for well-balanced schemes on non-resonant scalar balance laws. (English) Zbl 1288.65131
The paper deals with the numerical approximation of the non-resonant balance law
\[
\partial_t u+\partial_x f(u)=k(x)g(u),\quad u(0,x)=u_0(x),
\]
under the assumption \(\pm f^{\prime}(u) \geq \nu>0\).
The authors discuss the qualitative difference between time-splitting and well-balanced difference schemes and give the estimates showing the exponential error growth in time for the first ones and the linear growth for the second ones. The theoretical considerations are confirmed by the numerical experiments.
The authors discuss the qualitative difference between time-splitting and well-balanced difference schemes and give the estimates showing the exponential error growth in time for the first ones and the linear growth for the second ones. The theoretical considerations are confirmed by the numerical experiments.
Reviewer: Iwan Gawriljuk (Eisenach)
MSC:
| 65M15 | Error bounds for initial value and initial-boundary value problems involving PDEs |
| 65M06 | Finite difference methods for initial value and initial-boundary value problems involving PDEs |
| 35L65 | Hyperbolic conservation laws |
Keywords:
non-resonance balance law; well-balanced Godunov scheme; error estimates; wave-front tracking algorithm; numerical experimentsReferences:
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