Derive L-2-error bounds for Lax-Friedrichs schemes for discontinuous solutions oflinear hyperbolic convection equations.It is known that the Lax-Friedrichs scheme is a firstorder scheme.Analyzes convergent rate of the...Derive L-2-error bounds for Lax-Friedrichs schemes for discontinuous solutions oflinear hyperbolic convection equations.It is known that the Lax-Friedrichs scheme is a firstorder scheme.Analyzes convergent rate of the scheme through its modified equations andshows that the first order Lax-Friedrichs scheme to approach BV solutions of the convectionequation has L￣2-error bounds of O(△x￣(1/4)),where △x is the discrete mesh length.Nemericalexperiments are presented and numerical results justify the theoretical analysis.展开更多
The use of the finite finite element method leads to replace the initial domain by an approach- ing domain.In part I,the uniform validity of the friedrichs’and Korn’s inequalities in these ap- proaching domains will...The use of the finite finite element method leads to replace the initial domain by an approach- ing domain.In part I,the uniform validity of the friedrichs’and Korn’s inequalities in these ap- proaching domains will be proved under some appropriate assumptions.展开更多
Respected Mr.Ji Bingxuan,President of Chinese Association for International Understanding,On September 28,2021,Chinese Association for International Understanding (CAFIU) celebrated its 40th anniversary.The Friedrich ...Respected Mr.Ji Bingxuan,President of Chinese Association for International Understanding,On September 28,2021,Chinese Association for International Understanding (CAFIU) celebrated its 40th anniversary.The Friedrich Ebert Stiftung(FES) is privileged to establish and maintain a longterm friendship with CAFIU during its 40 years of glorious history.On behalf of FES and in my own name,I would like to extend heartfelt congratulations to you and your colleagues on this important day.展开更多
On January 13th,the Chinese Association for International Understanding(CAFIU)and the Friedrich-Ebert-Stiftung(FES)jointly held a Webinar themed Promoting People-to-People and Cultural Exchanges and Mutual Learning am...On January 13th,the Chinese Association for International Understanding(CAFIU)and the Friedrich-Ebert-Stiftung(FES)jointly held a Webinar themed Promoting People-to-People and Cultural Exchanges and Mutual Learning among Civilisations,Enhancing Mutual Understanding and Friendship between China and Germany.展开更多
We give a brief discussion of some of the contributions of Peter Lax to Com- putational Fluid Dynamics. These include the Lax-Friedrichs and Lax-Wendroff numerical schemes. We also mention his collaboration in the 198...We give a brief discussion of some of the contributions of Peter Lax to Com- putational Fluid Dynamics. These include the Lax-Friedrichs and Lax-Wendroff numerical schemes. We also mention his collaboration in the 1983 HLL Riemann solver. We de- velop two-dimensional Lax-Friedrichs and Lax-Wendroff schemes for the Lagrangian form of the Euler equations on triangular grids. We apply a composite scheme that uses a Lax- Friedrichs time step as a dissipative filter after several Lax-Wendroff time steps. Numerical results for Noh＇s infinite strength shock problem, the Sedov blast wave problem, and the Saltzman piston problem are presented.展开更多
A fluid dynamic traffic flow model based on a non-linear velocity-density function is considered. The model provides a quasi-linear first order hyperbolic partial differential equation which is appended with initial a...A fluid dynamic traffic flow model based on a non-linear velocity-density function is considered. The model provides a quasi-linear first order hyperbolic partial differential equation which is appended with initial and boundary data and turns out an initial boundary value problem (IBVP). A first order explicit finite difference scheme of the IBVP known as Lax-Friedrich’s scheme for our model is presented and a well-posedness and stability condition of the scheme is established. The numerical scheme is implemented in order to perform the numerical features of error estimation and rate of convergence. Fundamental diagram, density, velocity and flux profiles are presented.展开更多
文摘Derive L-2-error bounds for Lax-Friedrichs schemes for discontinuous solutions oflinear hyperbolic convection equations.It is known that the Lax-Friedrichs scheme is a firstorder scheme.Analyzes convergent rate of the scheme through its modified equations andshows that the first order Lax-Friedrichs scheme to approach BV solutions of the convectionequation has L￣2-error bounds of O(△x￣(1/4)),where △x is the discrete mesh length.Nemericalexperiments are presented and numerical results justify the theoretical analysis.
基金Programme Sino-Francais de Recherche Avanc es(PRA)and the Natural ScienceFoundations of China
文摘The use of the finite finite element method leads to replace the initial domain by an approach- ing domain.In part I,the uniform validity of the friedrichs’and Korn’s inequalities in these ap- proaching domains will be proved under some appropriate assumptions.
文摘Respected Mr.Ji Bingxuan,President of Chinese Association for International Understanding,On September 28,2021,Chinese Association for International Understanding (CAFIU) celebrated its 40th anniversary.The Friedrich Ebert Stiftung(FES) is privileged to establish and maintain a longterm friendship with CAFIU during its 40 years of glorious history.On behalf of FES and in my own name,I would like to extend heartfelt congratulations to you and your colleagues on this important day.
文摘On January 13th,the Chinese Association for International Understanding(CAFIU)and the Friedrich-Ebert-Stiftung(FES)jointly held a Webinar themed Promoting People-to-People and Cultural Exchanges and Mutual Learning among Civilisations,Enhancing Mutual Understanding and Friendship between China and Germany.
基金performed under the auspices of the National Nuclear Security Administration of the US Department of Energy at Los Alamos National Laboratory under Contract No.DE-AC52-06NA25396supported in part by the Czech Science Foundation GrantP205/10/0814the Czech Ministry of Education grants MSM 6840770022 and LC528
文摘We give a brief discussion of some of the contributions of Peter Lax to Com- putational Fluid Dynamics. These include the Lax-Friedrichs and Lax-Wendroff numerical schemes. We also mention his collaboration in the 1983 HLL Riemann solver. We de- velop two-dimensional Lax-Friedrichs and Lax-Wendroff schemes for the Lagrangian form of the Euler equations on triangular grids. We apply a composite scheme that uses a Lax- Friedrichs time step as a dissipative filter after several Lax-Wendroff time steps. Numerical results for Noh＇s infinite strength shock problem, the Sedov blast wave problem, and the Saltzman piston problem are presented.
文摘A fluid dynamic traffic flow model based on a non-linear velocity-density function is considered. The model provides a quasi-linear first order hyperbolic partial differential equation which is appended with initial and boundary data and turns out an initial boundary value problem (IBVP). A first order explicit finite difference scheme of the IBVP known as Lax-Friedrich’s scheme for our model is presented and a well-posedness and stability condition of the scheme is established. The numerical scheme is implemented in order to perform the numerical features of error estimation and rate of convergence. Fundamental diagram, density, velocity and flux profiles are presented.
