非线性退化抛物方程的有限体积格式
A finite volume scheme for nonlinear degenerate parabolic equations
AI总结：
针对非线性退化抛物方程，提出一种保持稳态且具有二阶空间精度的有限体积格式，并通过数值实验验证了其在退化和非退化情况下的高精度和长时间渐近保持效率。
摘要：
我们针对非线性退化抛物方程提出了一种二阶有限体积格式。对于其中一些模型（如多孔介质方程、半导体的漂移-扩散系统等），已经证明瞬态解随时间趋于无穷时会收敛到稳态。本格式保持稳态，并提供令人满意的长时间行为。此外，即使在退化情况下，该格式仍然有效且在空间上具有二阶精度。在描述数值格式后，我们展示了若干数值结果，这些结果确认了在多种退化和非退化情况下的高阶精度，并强调了保持长时间渐近的效率。
英文摘要：
We propose a second order finite volume scheme for nonlinear degenerate parabolic equations. For some of these models (porous media equation, drift-diffusion system for semiconductors, ...) it has been proved that the transient solution converges to a steady-state when time goes to infinity. The present scheme preserves steady-states and provides a satisfying long-time behavior. Moreover, it remains valid and second-order accurate in space even in the degenerate case. After describing the numerical scheme, we present several numerical results which confirm the high-order accuracy in various regime degenerate and non degenerate cases and underline the efficiency to preserve the large-time asymptotic.
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