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A Local Discontinuous Galerkin Method for Two-Dimensional Time Fractional Diffusion Equations

Communications on Applied Mathematics and Computation 2020年第4期2卷 689-709页

作者： Somayeh Yeganeh Reza Mokhtari Jan SHesthaven Department of Mathematical Sciences Isfahan University of TechnologyIsfahan 84156-83111Iran epfl-sb-mathices-mcss École Polytechnique Fédéral de Lausanne1015 LausanneSwitzerland

For two-dimensional(2D)time fractional diffusion equations,we construct a numerical method based on a local discontinuous Galerkin(LDG)method in space and a finite differ-ence scheme in *** investigate the numerical stability and convergence of the method for both rectangular and triangular meshes and show that the method is unconditionally *** results indicate the effectiveness and accuracy of the method and con-firm the analysis.

关键词： Two-dimensional(2D)time fractional difusion equation Local discontinuous Galerkin method(LDG) Numerical stability Convergence analysis

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Modeling 3D Magma Dynamics Using a Discontinuous Galerkin Method

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Communications in Computational Physics 2015年第6期18卷 230-246页

作者： Seshu Tirupathi Jan S.Hesthaven Yan Liang Division of Applied Mathematics Brown UniversityProvidenceRI 02912USA IBM Research DublinDamastown Industrial ParkMulhuddartDublin 15Ireland epfl-sb-MATHICSE-mcss Ecole Polytechnique Fédérale de Lausanne(EPFL)LausanneSwitzerland Department of Geological Sciences Brown UniversityProvidenceRI 02912USA

Discontinuous Galerkin(DG)and matrix-free finite element methods with a novel projective pressure estimation are combined to enable the numerical modeling of magma dynamics in 2D and 3D using the library *** physical model is an advection-reaction type system consisting of two hyperbolic equations to evolve porosity and soluble mineral abundance at local chemical equilibrium and one elliptic equation to recover global pressure.A combination of a discontinuous Galerkin method for the advection equations and a finite element method for the elliptic equation provide a robust and efficient solution to the channel regime problems of the physical system in 3D.A projective and adaptively applied pressure estimation is employed to significantly reduce the computational wall time without impacting the overall physical reliability in the modeling of important features of melt segregation,such as melt channel bifurcation in 2D and 3D time dependent simulations.

关键词： magma dynamics discontinuous Galerkin method finite element method matrixfree method

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Characterization of image spaces of Riemann-Liouville fractional integral operators on Sobolev spaces W^(m,p)(Ω)

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Science China Mathematics 2021年第12期64卷 2611-2636页

作者： Lijing Zhao Weihua Deng Jan S.Hesthaven School of Mathematics and Statistics Northwestern Polytechnical UniversityXi'an 710129China School of Mathematics and Statistics Gansu Key Laboratory of Applied Mathematics and Complex SystemsLanzhou UniversityLanzhou 730000China epfl-sb-MATHICSE-mcss Ecole Polytechnique Federale de LausanneLausanne CH-1015Switzerland

Fractional operators are widely used in mathematical models describing abnormal and nonlocal *** there are extensive numerical methods for solving the corresponding model problems,theoretical analysis such as the regularity result,or the relationship between the left-side and right-side fractional operators is seldom *** of considering the fractional derivative spaces,this paper starts from discussing the image spaces of Riemann-Liouville fractional integrals of L_(p)(Ω) functions,since the fractional derivative operators that are often used are all *** the high regularity situation-the image spaces of Riemann-Liouville fractional integral operators on the W^(m,p)(Ω) space is *** characterizations of the defined spaces,as well as those of the intersection of the left-side and right-side spaces are *** behavior of the functions in the defined spaces at both the nearby boundary point/points and the points in the domain is demonstrated in a clear ***,tempered fractional operators are shown to be reciprocal to the corresponding Riemann-Liouville fractional operators,which is expected to contribute some theoretical support for relevant numerical ***,we also provide some instructions on how to take advantage of the introduced spaces when numerically solving fractional equations.

关键词： image space Riemann-Liouville integral regularity property approximation

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公法契约之控制─从公私合伙架构谈起

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行政法学研究 2012年第1期 136-144页

作者：李训民政治大学国关中心mcss经济安全组

针对公私合伙制度(PPPs)下之契约,探究其系公法契约或是私法契约,具有实际意义。英国、德国及美国在公私合伙制度下之发展进程,值得关注;特别是英国成功发展的PPPs,建构"公法下之政府契约"及"私法下之政府契约"之模式足资赞许;德国针对P... 详细信息

针对公私合伙制度(PPPs)下之契约,探究其系公法契约或是私法契约,具有实际意义。英国、德国及美国在公私合伙制度下之发展进程,值得关注;特别是英国成功发展的PPPs,建构"公法下之政府契约"及"私法下之政府契约"之模式足资赞许;德国针对PPPs下之投资契约,是否适合置入于行政程序法下之行政性契约,相关立法沿革,值得注意与效法;而美国行政任务私有化后,行政机关对外购买服务,公权力充分与私部门分享,而未建构监督与契约治理机制,堪致忧虑,特别是契约外包之下,相关法律不禁止境外转包,则服务之质量与法律正当性受到质疑。

关键词：公私合伙政府契约行政任务私有化境外转包

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Overview of the South China Sea Monsoon Experiment

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Advances in Atmospheric Sciences 2004年第3期21卷 343-360页

作者：丁一汇李崇银柳艳菊 National Climate Center China Meteorological Administration Beijing 100081 State Key Laboratory of Numerical Modeling for Atmospheric Sciences and Geophysical Fluid Dynamics Institute of Atmospheric Physics Chinese Academy of Sciences Beijing 100029 National Climate Center China Meteorological Administration Beijing 100081 State Key Laboratory of Numerical Modeling for Atmospheric Sciences and Geophysical Fluid DynamicsInstitute of Atmospheric Physics Chinese Academy of Sciences Beijing 100029he present paper gives an overview of the key project " South China Sea Monsoon Experiment (SCSMEX)" operated by the Ministry of Science and Technology of China during the period of 1996-2001. The SCSMEX is a joint atmospheric and oceanic field experiment which aims to better understand the onset maintenance and variability of the summer monsoon over the South China Sea (SCS). It is a large-scale international effort with many participating countries and regions cooperatively involved in this experiment. With the field observation in May-August 1998 a large amount of meteorological and oceanic data was acquired which provides excellent datasets for the study of the SCS monsoon and the East Asian monsoon and their interaction with the ocean. The preliminary research achievements are as follows. (1) The earliest onset of the Asian monsoon over the SCS and Indo-China Peninsula has been well documented. Prom the viewpoint of the synoptic process its onset is closely related to the early rapid development of a twin cyclone to the east of Sri Lanka. The conceptual modei of the SCS monsoon onset in 1998 was put forward. The 50-year time series of the SCS monsoon onset date was also made. (2) Two major modes namely the 30-60-day and 10-20-day oscillations were ascertained. The influences of the abnormal SCS monsoon on the precipitation over eastern China and its modes were identifled. A strong (weak) monsoon over the SCS usually leads to less (more) precipitation over the middle and lower reaches of the Yangtze River

The present paper gives an overview of the key project ' South China Sea Monsoon Experiment (SCSMEX)' operated by the Ministry of Science and Technology of China during the period of 1996-2001. The SCSMEX is a joint atmospheric and oceanic field experiment which aims to better understand the onset, maintenance, and variability of the summer monsoon over the South China Sea (SCS). It is a large-scale international effort with many participating countries and regions cooperatively involved in this experiment. With the field observation in May-August 1998, a large amount of meteorological and oceanic data was acquired, which provides excellent datasets for the study of the SCS monsoon and the East Asian monsoon and their interaction with the ocean. The preliminary research achievements are as follows. (1) The earliest onset of the Asian monsoon over the SCS and Indo-China Peninsula has been well documented. Prom the viewpoint of the synoptic process, its onset is closely related to the early rapid development of a twin cyclone to the east of Sri Lanka. The conceptual modei of the SCS monsoon onset in 1998 was put forward. The 50-year time series of the SCS monsoon onset date was also made. (2) Two major modes, namely the 30-60-day and 10-20-day oscillations were ascertained. The influences of the abnormal SCS monsoon on the precipitation over eastern China and its modes were identifled. A strong (weak) monsoon over the SCS usually leads to less (more) precipitation over the middle and lower reaches of the Yangtze River basin, and more (less) precipitation in North China. (3) During the monsoon onset over the SCS, a wide variety of organized mesoscale convective systems (mcss) were observed by a Doppler radar array deployed over the northern SCS. The relationship between large-scale circulations and mcss during the monsoon onset process in 1998 was clearly revealed. It was suggested that there is a kind of positive feedback mechanism between large-scale circulations and

关键词： field experiment South China Sea monsoon low frequency oscillation (LFO) meso scale convective systems (MSCs) air-sea interaction numerical simulation

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