非线性强单调问题的数值均匀化
Numerical homogenization for nonlinear strongly monotone problems
摘要：
在这项工作中，我们介绍和分析了一个新的多尺度方法的精神，强非线性单调方程的局部正交分解。通过求解线性局部细尺度问题构造了一个问题适应的多尺度空间，并将其应用于广义有限元法。精细尺度问题的线性允许它们的本地化，而且，使该方法非常有效地使用。新方法给出了线性化误差的最优先验误差估计。所得结果既不需要对系数作周期性或尺度分离等结构性假设，也不要求解具有更高的正则性。从理论和实践上讨论了不同线性化策略的效果。包括定常Richards方程在内的几个数值算例证实了理论的正确性，并强调了方法的适用性。
英文摘要：
In this work we introduce and analyze a new multiscale method for strongly nonlinear monotone equations in the spirit of the Localized Orthogonal Decomposition. A problem-adapted multiscale space is constructed by solving linear local fine-scale problems which is then used in a generalized finite element method. The linearity of the fine-scale problems allows their localization and, moreover, makes the method very efficient to use. The new method gives optimal a priori error estimates up to linearization errors. The results neither require structural assumptions on the coefficient such as periodicity or scale separation nor higher regularity of the solution. The effect of different linearization strategies is discussed in theory and practice. Several numerical examples including stationary Richards equation confirm the theory and underline the applicability of the method.
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。
