16 Result(s)
within
Article
Jian-Guo Liu
Computational Mathematics and Numerical Analysis
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Article
On the Dynamics of the Boundary Vorticity for Incompressible Viscous Flows
The dynamical equation of the boundary vorticity has been obtained, which shows that the viscosity at a solid wall is doubled as if the fluid became more viscous at the boundary. For certain viscous flows the ...
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Article
Open AccessUniform spectral convergence of the stochastic Galerkin method for the linear transport equations with random inputs in diffusive regime and a micro–macro decomposition-based asymptotic-preserving method
In this paper we study the stochastic Galerkin approximation for the linear transport equation with random inputs and diffusive scaling. We first establish uniform (in the Knudsen number) stability results in ...
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Article
Explicit and Implicit TVD Schemes for Conservation Laws with Caputo Derivatives
In this paper, we investigate numerical approximations of the scalar conservation law with the Caputo derivative, which introduces the memory effect. We construct the first order and the second order explicit ...
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Article
Open AccessPropagation of chaos for large Brownian particle system with Coulomb interaction
We investigate a system of N Brownian particles with the Coulomb interaction in any dimension \(d\ge 2\) ...
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Article
A Note on \(L^{\infty}\) -Bound and Uniqueness to a Degenerate Keller-Segel Model
In this note we establish the uniform L ∞
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Article
Simple Finite Element Numerical Simulation of Incompressible Flow Over Non-rectangular Domains and the Super-Convergence Analysis
In this paper, we apply a simple finite element numerical scheme, proposed in an earlier work (Liu in Math Comput 70(234):579–593, 2000), to perform a high resolution numerical simulation of incompressible flow o...
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Article
A Note on Aubin-Lions-Dubinskiĭ Lemmas
Strong compactness results for families of functions in seminormed nonnegative cones in the spirit of the Aubin-Lions-Dubinskiĭ lemma are proven, refining some recent results in the literature. The first theor...
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Article
A Local Pressure Boundary Condition Spectral Collocation Scheme for the Three-Dimensional Navier–Stokes Equations
A spectral collocation scheme for the three-dimensional incompressible \(({\varvec{u}},p)\) ...
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Article
A Note on the Subcritical Two Dimensional Keller-Segel System
The existence of solution for the 2D-Keller-Segel system in the subcritical case, i.e. when the initial mass is less than 8π, is reproved. Instead of using the entropy in the free energy and free energy dissipati...
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Article
A modified BFGS method and its superlinear convergence in nonconvex minimization with general line search rule
In this paper, a modification of the BFGS algorithm for unconstrained nonconvex optimization is proposed. The idea of the algorithm is to modify the approximate Hessian matrix for obtaining the descent directi...
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Article
Global convergence of a modified BFGS-type method for unconstrained non-convex minimization
To the unconstrained programme of non-convex function, this article give a modified BFGS algorithm associated with the general line search model. The idea of the algorithm is to modify the approximate Hessian ...
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Article
Global convergence properties of two modified BFGS-type methods
This article studies a modified BFGS algorithm for solving smooth unconstrained strongly convex minimization problem. The modified BFGS method is based on the new quasi-Newton equation Bk+1sk=yk where yk*, =yk + ...
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Article
An two phase abs method for solving over determined systems of linear inequalities
The method, called the Multi-Stage ABS algorithm, for solving the over-determined linear inequalities system and the system combined with the over-determined linear inequalities and the equations is presented....
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Global convergence properties of the modified BFGS method associating with general line search model
To the unconstrained programme of non-convex function, this article give a modified BFGS algorithm. The idea of the algorithm is to modify the approximate Hessian matrix for obtaining the descent direction and...
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Article
Concepts and Application of Time-Limiters to High Resolution Schemes
A new class of implicit high-order non-oscillatory time integration schemes is introduced in a method-of-lines framework. These schemes can be used in conjunction with an appropriate spatial discretization sch...
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Article
A Fourth Order Scheme for Incompressible Boussinesq Equations
A fourth order finite difference method is presented for the 2D unsteady viscous incompressible Boussinesq equations in vorticity-stream function formulation. The method is especially suitable for moderate to ...
