报告人：李步扬（香港理工大学）

报告题目：A-stable time discretization preserve maximal parabolic regularity

报告摘要：It is shown that for a parabolic problem with maximal $L^p$-regularity (for $1 < p < \infty$), the time discretization by a linear multistep method or Runge-Kutta method has maximal $\ell^p$-regularity uniformly in the stepsize if the method is A-stable. In particular, the implicit Euler method, the Crank-Nicolson method, the second-order backward difference formula, and the Radau IIA and Gauss Runge–Kutta methods of all orders preserve maximal regularity. The $A(\alpha)$-stable higher-order BDF methods have maximal $\ell^p$-regularity under an $R$-boundedness condition in a larger sector. These results are also extended to time-stepping methods for time-fractional evolution equations, including the L1 scheme, convolution quadratures generated by the A-stable BDFs, explicit Euler method, and the fractional version of the Crank-Nicolson method. As an illustration of the use of maximal regularity in the error analysis of discretized nonlinear parabolic equations, it is shown how error bounds are obtained without using any growth condition on the nonlinearity.

报告人简介：2012年于香港城市大学获得博士学位，2015-2016年为德国University of Tuebingen洪堡学者，主要研究方向为微分方程数值解。至今《SIAM J. Numer. Anal.》《Numer. Math.》《Math. Comput.》《J. Comput. Phys.》等著名计算数学SCI杂志发表论文30余篇。

报告时间：2017年6月16日（星期五）上午 9:30-10:30

报告地点：科技楼702