张镭 教授 （ 上海交通大学 ）

谢和虎 研究员

Numerical homogenization for multiscale elliptic PDEs

6 月 23 日（周四）下午 16:00-17:00 腾讯会议（ID：530 4940 3354）

The field of numerical homogenization concerns the numerical approximation of the solution space of, for example, divergence form elliptic equation with L^{\infty} coefficients by a finite-dimensional space. This problem is motivated by the fact that standard methods such as finite-element method with piecewise polynomial elements can perform arbitrarily badly for PDEs with rough coefficients. Some numerical homogenization methods are developed from classical homogenization concepts such as periodic homogenization and scale separation, however, one of the main objectives of numerical homogenization is to achieve a numerical approximation of the solution space of the equation with arbitrary rough coefficients. In this lecture, I will introduce some basic ideas for the numerical homogenization of elliptic multiscale PDEs, and sketch a review for some recent developments.