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Central local discontinuous galerkin methods on overlapping cells for diffusion equations

Yingjie Liu;  Chi-Wang Shu;  Eitan Tadmor;  Mengping Zhang — 2011

ESAIM: Mathematical Modelling and Numerical Analysis

In this paper we present two versions of the central local discontinuous Galerkin (LDG) method on overlapping cells for solving diffusion equations, and provide their stability analysis and error estimates for the linear heat equation. A comparison between the traditional LDG method on a single mesh and the two versions of the central LDG method on overlapping cells is also made. Numerical experiments are provided to validate the quantitative conclusions from the analysis and to support conclusions...

Central local discontinuous galerkin methods on overlapping cells for diffusion equations

Yingjie Liu;  Chi-Wang Shu;  Eitan Tadmor;  Mengping Zhang — 2011

ESAIM: Mathematical Modelling and Numerical Analysis

In this paper we present two versions of the central local discontinuous Galerkin (LDG) method on overlapping cells for solving diffusion equations, and provide their stability analysis and error estimates for the linear heat equation. A comparison between the traditional LDG method on a single mesh and the two versions of the central LDG method on overlapping cells is also made. Numerical experiments are provided to validate the quantitative conclusions from the analysis and to support conclusions...

stability analysis of the central discontinuous Galerkin method and a comparison between the central and regular discontinuous Galerkin methods

Yingjie Liu;  Chi-Wang Shu;  Eitan Tadmor;  Mengping Zhang — 2008

ESAIM: Mathematical Modelling and Numerical Analysis


We prove stability and derive error estimates for the recently introduced central discontinuous Galerkin method, in the context of linear hyperbolic equations with possibly discontinuous solutions. A comparison between the central discontinuous Galerkin method and the regular discontinuous Galerkin method in this context is also made. Numerical experiments are provided to validate the quantitative conclusions from the analysis.

Existence and non-existence of global solutions for nonlinear hyperbolic equations of higher order

Guo Wang Chen;  Shu Bin Wang — 1995

Commentationes Mathematicae Universitatis Carolinae

The existence and uniqueness of classical global solution and blow up of non-global solution to the first boundary value problem and the second boundary value problem for the equation u t t - α u x x - β u x x t t = ϕ ( u x ) x are proved. Finally, the results of the above problem are applied to the equation arising from nonlinear waves in elastic rods u t t - a 0 + n a 1 ( u x ) n - 1 u x x - a 2 u x x t t = 0 .

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