关于某些有限体积格式的离散泛函不等式
On discrete functional inequalities for some finite volume schemes
AI总结：
利用BV空间嵌入证明有限体积网格上任意边界值的离散Gagliardo-Nirenberg-Sobolev和Poincaré-Sobolev不等式，并应用于离散对偶有限体积格式。
摘要：
我们证明了在有限体积网格上具有任意边界值的若干离散Gagliardo-Nirenberg-Sobolev和Poincaré-Sobolev不等式。我们的方法的关键是使用空间$BV(Ω)$到$L^{N/(N-1)}(Ω)$的连续嵌入，其中$Ω\subset \mathbb{R}^{N}$是Lipschitz域，$N \geq 2$。最后，我们给出了在用于逼近非线性和非各向同性椭圆和抛物问题的离散对偶有限体积（DDFV）格式中的几个应用。
英文摘要：
We prove several discrete Gagliardo-Nirenberg-Sobolev and Poincaré-Sobolev inequalities for some approximations with arbitrary boundary values on finite volume meshes. The keypoint of our approach is to use the continuous embedding of the space $BV(Ω)$ into $L^{N/(N-1)}(Ω)$ for a Lipschitz domain $ Ω\subset \mathbb{R}^{N}$, with $N \geq 2$. Finally, we give several applications to discrete duality finite volume (DDFV) schemes which are used for the approximation of nonlinear and non isotropic elliptic and parabolic problems.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
