论文标题
非散发形式中椭圆均质问题问题的最佳收敛速率：分析和数值插图
Optimal convergence rates for elliptic homogenization problems in nondivergence-form: analysis and numerical illustrations
论文作者
论文摘要
我们研究了形式$ -a（x/\ varepsilon）的线性椭圆方程的定期均质化中的最佳收敛速率：d^2 u^{\ varepsilon} = f $受均匀的dirichlet边界条件的约束。我们表明，$ u^{\ varepsilon} $收敛的最佳速率对$ w^{1，p} $ - norm-norm-norm是$ \ m athcal {o}（\ varepsilon）$中相应同质化问题的解决方案。我们进一步获得了最佳的梯度和Hessian界限，并在$ l^p $ -norm中考虑了校正条款。然后，我们提供一个显式$ C $ -BAD扩散矩阵，并使用它执行各种数值实验，以证明获得的速率的最佳性。
We study optimal convergence rates in the periodic homogenization of linear elliptic equations of the form $-A(x/\varepsilon):D^2 u^{\varepsilon} = f$ subject to a homogeneous Dirichlet boundary condition. We show that the optimal rate for the convergence of $u^{\varepsilon}$ to the solution of the corresponding homogenized problem in the $W^{1,p}$-norm is $\mathcal{O}(\varepsilon)$. We further obtain optimal gradient and Hessian bounds with correction terms taken into account in the $L^p$-norm. We then provide an explicit $c$-bad diffusion matrix and use it to perform various numerical experiments, which demonstrate the optimality of the obtained rates.
