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Superconvergence of Direct Discontinuous Galerkin Methods:eigen-structure Analysis Based on Fourier Approach

Communications on Applied Mathematics and Computation 2024年第1期6卷 257-278页

作者： Xuechun Liu Haijin Wang Jue Yan Xinghui Zhong School of Mathematical Sciences Zhejiang UniversityHangzhou310027ZhejiangChina School of Science Nanjing University of Posts and TelecommunicationsNanjing210023JiangsuChina Department of Mathematics Iowa State UniversityAmes50011IAUSA

This paper investigates superconvergence properties of the direct discontinuous Galerkin(DDG)method with interface corrections and the symmetric DDG method for diffusion *** apply the Fourier analysis technique to symbolically compute eigenvalues and eigenvectors of the amplification matrices for both DDG methods with different coefficient settings in the numerical *** on the eigen-structure analysis,we carry out error estimates of the DDG solutions,which can be decomposed into three parts:(i)dissipation errors of the physically relevant eigenvalue,which grow linearly with the time and are of order 2k for P^(k)(k=2,3)approximations;(ii)projection error from a special projection of the exact solution,which is decreasing over the time and is related to the eigenvector corresponding to the physically relevant eigenvalue;(iii)dissipative errors of non-physically relevant eigenvalues,which decay exponentially with respect to the spatial mesh sizeΔ*** observe that the errors are sensitive to the choice of the numerical flux coefficient for even degree P^(2)approximations,but are not for odd degree P^(3)*** experiments are provided to verify the theoretical results.

关键词： Direct discontinuous Galerkin(DDG)method with interface correction Symmetric DDG method Superconvergence Fourier analysis eigen-structure

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Inseparability of Min-Max Systems

Inseparability of Min-Max Systems

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第二十二届中国控制会议

作者： Zhao Qianchuan Department of Automation, Tsinghua University, Beijing 100084

＜正＞Min-max systems, or min-max-plus systems are algebraic models of Discrete Event Dynamic Systems. They are non-linear extension of the well known linear max-plus system models. In this paper, we survey our recent research results related to the structural property "inseparability" of min-max systems proposed in [24]. It turns out inseparability has very interesting relationship to many aspects of min-max systems. It has been applied to the stabilization of min-max systems. It also has interesting implications to other important research areas including bio-informatics and artificial neural networks.

关键词： Min-max systems eigen-structure Inseparability Structural property.

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