Abstract
The main goal of the present Chapter is to emphasize the qualitative difference between Time-Splitting (TS, also called Fractional Step, FS) and Well-Balanced (WB) numerical schemes when it comes to computing the entropy solution [26] of a simple scalar, yet non-resonant, balance law:
A child of five would understand this. Send someone to fetch a child of five.
Groucho Marx
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Notes
- 1.
Observe that it would already be problematic for an homogeneous scalar conservation law in which k ≡ 0 because its L 1 error is known to increase in time like \( \mathcal{O} \) (\( \sqrt{t}, \)) as explained in e.g. [36].
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Gosse, L. (2013). Lyapunov Functional for Linear Error Estimates. In: Computing Qualitatively Correct Approximations of Balance Laws. SIMAI Springer Series, vol 2. Springer, Milano. https://doi.org/10.1007/978-88-470-2892-0_3
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