<div style="text-align:justify;"> In this paper, the numerical solution and its error analysis of quasilinear singular perturbation two-point boundary value problems based on the principle of equidistr...<div style="text-align:justify;"> In this paper, the numerical solution and its error analysis of quasilinear singular perturbation two-point boundary value problems based on the principle of equidistribution are given. On the non-uniform grid of the uniformly distributed arc-length monitor function, the solution of the simple upwind scheme is obtained. It is proved that the adaptive simple upwind scheme based on the principle of equidistribution has uniform convergence for small perturbation parameters. Numerical experiments are carried out and the error analysis are confirmed. </div>展开更多
Games often provide a good introduction to interesting phenomena in mathematics. In this note, we examine three variations of an iterative sharing game played around a circular (or not so circular) table. More precise...Games often provide a good introduction to interesting phenomena in mathematics. In this note, we examine three variations of an iterative sharing game played around a circular (or not so circular) table. More precisely, for each variation, we study the tendency toward equal distribution among the players. In the first variation, the players have discrete amounts at each step. The second variation removes this restriction, and the third one considers an infinitely long table with an infinite number of players.展开更多
Let X=G/Γbe a homogeneous space with ambient group G containing the group H=(SO(n,1))^(k)and x∈X be such that Hx is dense in X.Given an analytic curve?:I=[a,b]→H,we will show that ifφsatisfies certain geometric co...Let X=G/Γbe a homogeneous space with ambient group G containing the group H=(SO(n,1))^(k)and x∈X be such that Hx is dense in X.Given an analytic curve?:I=[a,b]→H,we will show that ifφsatisfies certain geometric condition,then for a typical diagonal subgroup A={a(t):t∈R}■H the translates{a(t)?(I)x:t>0}of the curve?(I)x will tend to be equidistributed in X as t→+∞.The proof is based on Ratner's theorem and linearization technique.展开更多
Mesh adaptation is studied from the mesh control point of view.Two principles,equidistribution and alignment,are obtained and found to be necessary and sufficient for a complete control of the size,shape,and orientati...Mesh adaptation is studied from the mesh control point of view.Two principles,equidistribution and alignment,are obtained and found to be necessary and sufficient for a complete control of the size,shape,and orientation of mesh elements.A key component in these principles is the monitor function,a symmetric and positive definite matrix used for specifying the mesh information.A monitor function is defined based on interpolation error in a way with which an error bound is minimized on a mesh satisfying the equidistribution and alignment conditions.Algorithms for generating meshes satisfying the conditions are developed and two-dimensional numerical results are presented.展开更多
An adaptive moving mesh method is developed for the numerical solution of two-dimensional phase change problems modelled by the phase-field equations.The numerical algorithm is relatively simple and is shown to be mor...An adaptive moving mesh method is developed for the numerical solution of two-dimensional phase change problems modelled by the phase-field equations.The numerical algorithm is relatively simple and is shown to be more efficient than fixed grid methods.The phase-field equations are discretised by a Galerkin finite element method.An adaptivity criterion is used that ensures that the mesh spacing at the phase front scales with the diffuse interface thickness.展开更多
文摘<div style="text-align:justify;"> In this paper, the numerical solution and its error analysis of quasilinear singular perturbation two-point boundary value problems based on the principle of equidistribution are given. On the non-uniform grid of the uniformly distributed arc-length monitor function, the solution of the simple upwind scheme is obtained. It is proved that the adaptive simple upwind scheme based on the principle of equidistribution has uniform convergence for small perturbation parameters. Numerical experiments are carried out and the error analysis are confirmed. </div>
文摘Games often provide a good introduction to interesting phenomena in mathematics. In this note, we examine three variations of an iterative sharing game played around a circular (or not so circular) table. More precisely, for each variation, we study the tendency toward equal distribution among the players. In the first variation, the players have discrete amounts at each step. The second variation removes this restriction, and the third one considers an infinitely long table with an infinite number of players.
基金Supported by NSFC(Grant No.11801384)the Fundamental Research Funds for the Central Universities(Grant No.YJ201769)。
文摘Let X=G/Γbe a homogeneous space with ambient group G containing the group H=(SO(n,1))^(k)and x∈X be such that Hx is dense in X.Given an analytic curve?:I=[a,b]→H,we will show that ifφsatisfies certain geometric condition,then for a typical diagonal subgroup A={a(t):t∈R}■H the translates{a(t)?(I)x:t>0}of the curve?(I)x will tend to be equidistributed in X as t→+∞.The proof is based on Ratner's theorem and linearization technique.
基金supported in part by the NSF under grant DMS-0410545.
文摘Mesh adaptation is studied from the mesh control point of view.Two principles,equidistribution and alignment,are obtained and found to be necessary and sufficient for a complete control of the size,shape,and orientation of mesh elements.A key component in these principles is the monitor function,a symmetric and positive definite matrix used for specifying the mesh information.A monitor function is defined based on interpolation error in a way with which an error bound is minimized on a mesh satisfying the equidistribution and alignment conditions.Algorithms for generating meshes satisfying the conditions are developed and two-dimensional numerical results are presented.
文摘An adaptive moving mesh method is developed for the numerical solution of two-dimensional phase change problems modelled by the phase-field equations.The numerical algorithm is relatively simple and is shown to be more efficient than fixed grid methods.The phase-field equations are discretised by a Galerkin finite element method.An adaptivity criterion is used that ensures that the mesh spacing at the phase front scales with the diffuse interface thickness.
