Zhen-huan Teng

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It is proved that for scalar conservation laws, if the flux function is strictly convex, and if the entropy solution is piecewise smooth with finitely many discontinuities (which includes initial central rarefaction waves, initial shocks, possible spontaneous formation of shocks in a future time and interactions of all these patterns), then the error of(More)
The aim of this paper is to develop a fast numerical method for two-dimensional boundary integral equations of the first kind with logarithm kernels when the boundary of the domain is smooth and closed. In this case, the use of the conventional boundary element methods gives linear systems with dense matrix. In this paper, we demonstrate that the dense(More)
In this paper we study the zero reaction limit of the hyperbolic conservation law with stii source term @ t u + @ x f(u) = 1 u(1 ? u 2) : For the Cauchy problem to the above equation, we prove that as ! 0, its solution converges to piecewise constant (1) solution, where the two constants are the two stable local equilibrium. The constants are separated by(More)
This paper considers the viscous approximations to conservation laws with nonconvex flux function. It is shown that if the entropy solutions are piecewise smooth, then the rate of L1convergence is a fractional number in (0.5, 1]. This is in contrast to the corresponding result for the convex conservation laws. Numerical experiments indicate that the(More)
In this paper we address the questions of the convergence rate for approximate solutions to conservation laws with piecewise smooth solutions in a weighted W 1,1 space. Convergence rate for the derivative of the approximate solutions is established under the assumption that a weak pointwise-error estimate is given. In other words, we are able to convert(More)
We study the structure and smoothness of non-homogeneous convex conservation laws. The question regarding the number of smoothness pieces is addressed. It is shown that under certain conditions on the initial data the entropy solution has only a finite number of discontinuous curves. We also obtain some global estimates on derivatives of the piecewise(More)
In this paper we show that the monotone difference methods with smooth numerical fluxes possess superconvergence property when applied to strictly convex conservation laws with piecewise smooth solutions. More precisely, it is shown that not only the approximation solution converges to the entropy solution, its central difference also converges to the(More)
The initial value problem of convex conservation laws, which includes the famous Burgers’ (inviscid) equation, plays an important rule not only in theoretical analysis for conservation laws, but also in numerical computations for various numerical methods. For example, the initial value problem of the Burgers’ equation is one of the most popular benchmarks(More)
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