Speaker:Shen Jie,Professor, School of Mathematics, Purdue University

Date:October. 23, 2021

Time:9:00 a.m.

Location:Lecture Hall 924, Block B, Zhixin Building, Central Campus

Sponsor:School of Mathematics, Shandong University

Abstract:

Solutions for a large class of partial differential equations (PDEs) arising from sciences and engineering applications are required to be positive to be positive or within a specified bound. It is of critical importance that their numerical approximations preserve the positivity/bound at the discrete level, as violation of the positivity/bound preserving may render the discrete problems ill posed. I will review the existing approaches for constructing positivity/bound preserving schemes, and then present a new Lagrange multiplier approach for constructing a class of positivity/bound preserving schemes for parabolic type equations. The new approach introduces a space-time Lagrange multiplier to enforce the positivity/bound using the Karush-Kuhn-Tucker (KKT) conditions. We then use a predictor-corrector approach to construct a class of positivity/bound preserving schemes: with a generic semi-implicit or implicit scheme as the prediction step, and the correction step, which enforces the positivity/bound preserving, can be implemented with negligible cost. We shall present some stability/error analysis for our schemes under a general setting, and present ample numerical results to validate the new approach.

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https://www.view.sdu.edu.cn/info/1020/157983.htm