How accurate are solutions of optimal control problems?
Báo cáo viên: Professor Arnd Ro"sch (Universita"t Duisburg-Essen)

Thời gian: 10h45, Thứ 6, ngày 22 tháng 3 năm 2019

Địa điểm: Hội trường tầng 2, Nhà A6, Viện Toán học, 18 Hoàng Quốc Việt, Cầu Giấy, Hà Nội

Tóm tắt: Optimal control of partial differential equations is very important for a lot of technological processes. Usually, such problems are characterized by several mathematical difficulties: coupled systems of nonlinear equations, geometrical singularities and pointwise inequality constraints. Such problems can only solved numerically. Consequently, the question occur: How accurate are numerical solutions of optimal control problems?

In this talk I will only consider linear elliptic equations. After a short motivation I will give a short introduction to the theory of linear-quadratic optimal control problems. Next, I will discuss different approaches to discretize the problems.
The most simple approach gives the order $h$ of the mesh size.

More advanced methods increase the order to $h^2$. Recent results show that even order $h^4$ is possible.

In a separate part I will present the modifications which are needed for geometrical singularities like reentrant corners. The whole talk is illustrated by numerical experiments.

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