Lecturer:Chen Yanping

Abstract:

We investigate a posteriori error analysis for hybridizable disontinuous Galerkin methods for convection diffusion equations. A residual-type error estimator without any postprocessing solutions is proposed, and we prove that the error estimator is robust with respect to the error measured by an easily calculated energy norm in the sense that the efficiency and reliability constants are independent of the diffusion coefficient. Then the result and the method, that have been obtained and used for convection diffusion equations, are applied to linear-quadratic distributed optimal control problems governed by convection diffusion equations. We use the variational discretization concept for the approximation of control, and an efficient and reliable error estimator is obtained for the error measured by an energy norm. Note that the estimator is also robust in the sense that the ratio of the upper and lower bounds is independent of the diffusion coefficient. Finally, several examples are provided to validate the performance of the obtained error estimators.

Introduction to the Lecturer:

Professor II, Doctoral Supervisor, South China Normal University. She is a Pearl River Scholar Professor of Higher Education in Guangdong Province, and was granted special government allowance in 2004 by the State Council, selected into the first Program for New Century Excellent Talents in University of the Ministry of Education, and listed among the first Excellent University Key Teachers of the Ministry of Education in 2002. She received the Second Prize of Natural Science of the Ministry of Education in 2017, the Second Prize of Science and Technology of Guangdong Province in 2012, the First Prize of Natural Science of Hunan Province in 2011, the First Prize of Natural Science of the Ministry of Education in 2008, and the Second Prize of Science and Technology Progress of Hunan Province in 2004. She has the monographTheory of Efficient Algorithms for Optimal Control Problems(English version, China Science Publishing and Media Ltd., November 2015, funded by the National Publication Foundation and included in the Information and Computational Science Series) and textbooksTheory of Efficient Algorithms for Optimal Control Problems(English version),NumericalSolutionofPartialDifferentialEquationsandGuidelinesforAssessmentandInstructioninMathematicalModelingEducationpublished, and also has 264 academic papers published in SIAM Numer. Anal., Math. Comp. and other international top academic journals. She is the author of ESI highly cited papers, and has defended her position in the Elsevier list of highly cited scholars in China for 7 consecutive years from 2014 to 2020. She leads one Key Program, seven General Programs and one major research plan incubation program of National Natural Science Foundation of China.

Invitee:

Rui Hongxing, Professor from School of Mathematics

Time:

14:00 p.m., May 20 (Thursday)

Venue:

Academic Hall #924, Block B, Zhixin Building, Central Campus

Hosted by the School of Mathematics, Shandong University