The Experts below are selected from a list of 854619 Experts worldwide ranked by ideXlab platform
Zhi Zhou - One of the best experts on this subject based on the ideXlab platform.
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Numerical Analysis of nonlinear subdiffusion equations
SIAM Journal on Numerical Analysis, 2018Co-Authors: Bangti Jin, Zhi ZhouAbstract:We present a general framework for the rigorous Numerical Analysis of time-fractional nonlinear parabolic partial differential equations, with a fractional derivative of order $\alpha\in(0,1)$ in time. It relies on three technical tools: a fractional version of the discrete Gronwall type inequality, discrete maximal regularity, and regularity theory of nonlinear equations. We establish a general criterion for showing the fractional discrete Gronwall inequality and verify it for the L1 scheme and convolution quadrature generated by backward difference formulas. Further, we provide a complete solution theory, e.g., existence, uniqueness, and regularity, for a time-fractional diffusion equation with a Lipschitz nonlinear source term. Together with the known results of discrete maximal regularity, we derive pointwise $L^2(\Omega)$ norm error estimates for semidiscrete Galerkin finite element solutions and fully discrete solutions, which are of order $O(h^2)$ (up to a logarithmic factor) and $O(\tau^\alpha)$, ...
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Numerical Analysis of nonlinear subdiffusion equations
arXiv: Numerical Analysis, 2017Co-Authors: Bangti Jin, Zhi ZhouAbstract:We present a general framework for the rigorous Numerical Analysis of time-fractional nonlinear parabolic partial differential equations, with a fractional derivative of order $\alpha\in(0,1)$ in time. The framework relies on three technical tools: a fractional version of the discrete Gronwall-type inequality, discrete maximal regularity, and regularity theory of nonlinear equations. We establish a general criterion for showing the fractional discrete Gronwall inequality, and verify it for the L1 scheme and convolution quadrature generated by BDFs. Further, we provide a complete solution theory, e.g., existence, uniqueness and regularity, for a time-fractional diffusion equation with a Lipschitz nonlinear source term. Together with the known results of discrete maximal regularity, we derive pointwise $L^2(\Omega)$ norm error estimates for semidiscrete Galerkin finite element solutions and fully discrete solutions, which are of order $O(h^2)$ (up to a logarithmic factor) and $O(\tau^\alpha)$, respectively, without any extra regularity assumption on the solution or compatibility condition on the problem data. The sharpness of the convergence rates is supported by the Numerical experiments.
Seong Gil Kang - One of the best experts on this subject based on the ideXlab platform.
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Numerical Analysis on depressurization of high pressure carbon dioxide pipeline
Journal of the Korean Society for Marine Environment and Energy, 2016Co-Authors: Cheol Huh, Meang Ik Cho, Seong Gil KangAbstract:To inject huge amount of CO2 for CCS application, high pressure pipeline transport is accompanied. Rapid depressurization of CO2 pipeline is required in case of transient processes such as accident and maintenance. In this study, Numerical Analysis on the depressurization of high pressure CO2 pipeline was carried out. The predic- tion capability of the Numerical model was evaluated by comparing the benchmark experiments. The Numerical models well predicted the liquid-vapor two-phase depressurization. On the other hands, there were some limita- tions in predicting the temperature behavior during the supercritical, liquid phase and gaseous phase expansions.
Jin Xuesong - One of the best experts on this subject based on the ideXlab platform.
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Numerical Analysis method of wheel rail adhesion under water lubrication for high speed railway
Journal of Traffic and Transportation Engineering, 2012Co-Authors: Jin XuesongAbstract:Multigrid method was introduced into the calculation of wheel/rail adhesion under wet condition at high speed,and the influence of train speed and contact pressure on water film thickness was investigated under wet condition without thinking about surface roughness.Numerical Analysis result shows that surface roughness and water film thickness have same order,and surface roughness is not ignored.Partial lubrication theory was applied to study the contact characteristics of wheel and rail under water lubrication based on the Numerical Analysis result,and the relationship between train speed and adhesion coefficient was investigated.Computation result indicates that with the increase of train speed,adhesion coefficient decreases rapidly,and its values are below 0.1.The comparison of experimental result obtained by JD-1 testing machine at the simulation speeds of 60,90 and 120 km·h-1 and Numerical Analysis result shows that the maximum relative error of adhesion coefficient is less than 8%,so the Numerical Analysis method is accurate to estimate adhesion coefficient.3 tabs,5 figs,22 refs.
Bangti Jin - One of the best experts on this subject based on the ideXlab platform.
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Numerical Analysis of nonlinear subdiffusion equations
SIAM Journal on Numerical Analysis, 2018Co-Authors: Bangti Jin, Zhi ZhouAbstract:We present a general framework for the rigorous Numerical Analysis of time-fractional nonlinear parabolic partial differential equations, with a fractional derivative of order $\alpha\in(0,1)$ in time. It relies on three technical tools: a fractional version of the discrete Gronwall type inequality, discrete maximal regularity, and regularity theory of nonlinear equations. We establish a general criterion for showing the fractional discrete Gronwall inequality and verify it for the L1 scheme and convolution quadrature generated by backward difference formulas. Further, we provide a complete solution theory, e.g., existence, uniqueness, and regularity, for a time-fractional diffusion equation with a Lipschitz nonlinear source term. Together with the known results of discrete maximal regularity, we derive pointwise $L^2(\Omega)$ norm error estimates for semidiscrete Galerkin finite element solutions and fully discrete solutions, which are of order $O(h^2)$ (up to a logarithmic factor) and $O(\tau^\alpha)$, ...
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Numerical Analysis of nonlinear subdiffusion equations
arXiv: Numerical Analysis, 2017Co-Authors: Bangti Jin, Zhi ZhouAbstract:We present a general framework for the rigorous Numerical Analysis of time-fractional nonlinear parabolic partial differential equations, with a fractional derivative of order $\alpha\in(0,1)$ in time. The framework relies on three technical tools: a fractional version of the discrete Gronwall-type inequality, discrete maximal regularity, and regularity theory of nonlinear equations. We establish a general criterion for showing the fractional discrete Gronwall inequality, and verify it for the L1 scheme and convolution quadrature generated by BDFs. Further, we provide a complete solution theory, e.g., existence, uniqueness and regularity, for a time-fractional diffusion equation with a Lipschitz nonlinear source term. Together with the known results of discrete maximal regularity, we derive pointwise $L^2(\Omega)$ norm error estimates for semidiscrete Galerkin finite element solutions and fully discrete solutions, which are of order $O(h^2)$ (up to a logarithmic factor) and $O(\tau^\alpha)$, respectively, without any extra regularity assumption on the solution or compatibility condition on the problem data. The sharpness of the convergence rates is supported by the Numerical experiments.
Cheol Huh - One of the best experts on this subject based on the ideXlab platform.
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Numerical Analysis on depressurization of high pressure carbon dioxide pipeline
Journal of the Korean Society for Marine Environment and Energy, 2016Co-Authors: Cheol Huh, Meang Ik Cho, Seong Gil KangAbstract:To inject huge amount of CO2 for CCS application, high pressure pipeline transport is accompanied. Rapid depressurization of CO2 pipeline is required in case of transient processes such as accident and maintenance. In this study, Numerical Analysis on the depressurization of high pressure CO2 pipeline was carried out. The predic- tion capability of the Numerical model was evaluated by comparing the benchmark experiments. The Numerical models well predicted the liquid-vapor two-phase depressurization. On the other hands, there were some limita- tions in predicting the temperature behavior during the supercritical, liquid phase and gaseous phase expansions.
