التفاصيل البيبلوغرافية
| العنوان: |
Compactness estimates for difference schemes for conservation laws with discontinuous flux. |
| المؤلفون: |
Karlsen, Kenneth H1 (AUTHOR) kennethk@math.uio.no, Towers, John D2 (AUTHOR) |
| المصدر: |
IMA Journal of Numerical Analysis. Nov2024, Vol. 44 Issue 6, p3313-3353. 41p. |
| مصطلحات موضوعية: |
*DISCONTINUOUS coefficients, *CONSERVATION laws (Physics), *FINITE differences, *ENTROPY, *EQUATIONS, *CONSERVATION laws (Mathematics) |
| مستخلص: |
We establish quantitative compactness estimates for finite difference schemes used to solve nonlinear conservation laws. These equations involve a flux function |$f(k(x,t),u)$| , where the coefficient |$k(x,t)$| is |$BV$| -regular and may exhibit discontinuities along curves in the |$(x,t)$| plane. Our approach, which is technically elementary, relies on a discrete interaction estimate and one entropy function. While the details are specifically outlined for the Lax-Friedrichs scheme, the same framework can be applied to other difference schemes. Notably, our compactness estimates are new even in the homogeneous case (|$k\equiv 1$|). [ABSTRACT FROM AUTHOR] |
| قاعدة البيانات: |
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