No abstract uploaded!

In this paper, we develop and analyze an arbitrary Lagrangian-Eulerian discontinuous Galerkin (ALE-DG) method with a time-dependent approximation space for one dimensional conservation laws, which satisfies the geometric conservation law. For the semi-discrete ALE-DG method, when applied to nonlinear scalar conservation laws, a cell entropy inequality, L2 stability and error estimates are proven. More precisely, we prove the sub-optimal (k+1/2) convergence for monotone fluxes, and optimal (k+1) convergence for an upwind flux, when a piecewise P^k polynomial approximation space is used. For the fully-discrete ALE-DG method, the geometric conservation law and the local maximum principle are proven. Moreover, we state conditions for slope limiters, which ensure total variation stability of the method. Numerical examples show the capability of the method.

Jiang et al. (Transportation Research Part B, 2011, 45(2), 343-363) proposed a predictive continuum dynamic user-optimal (PDUO-C) model to investigate the dynamic characteristics of traffic flow and the corresponding route-choice behavior of travelers. The modeled region is a dense urban city, which is arbitrary in shape and has a single central business district (CBD). However, we argue that the model is not well posed due to an inconsistency in the route-choice strategy. To overcome this inconsistency, we revisit the PDUO-C problem, and construct an improved path-choice strategy. The improved model consists of a conservation law to govern the density, in which the flow direction is determined by the improved path-choice strategy, and a Hamilton-Jacobi equation to compute the total travel cost. The simultaneous satisfaction of both equations can be treated as a fixed-point problem. A self-adaptive method of successive averages (MSA) is proposed to solve this fixed-point problem. This method can automatically determine the optimal MSA step size using the least squares approach. Numerical examples are used to demonstrate the effectiveness of the model and the solution algorithm.

Variational models with \ell_1-norm based regularization, in particular total variation (TV) and its variants, have long been known to offer superior image restoration quality, but processing speed remained a bottleneck, preventing their widespread use in the practice of color image processing. In this paper, by extending the grayscale image deblurring algorithm proposed in [Y. Wang, J. Yang, W. Yin, and Y. Zhang, <i>SIAM J. Imaging Sci.</i>, 1 (2008), pp. 248272], we construct a simple and efficient algorithm for multichannel image deblurring and denoising, applicable to both within-channel and cross-channel blurs in the presence of additive Gaussian noise. The algorithm restores an image by minimizing an energy function consisting of an \ell_1-norm fidelity term and a regularization term that can be either TV, weighted TV, or regularization functions based on higher-order derivatives. Specifically, we use a multichannel

No abstract uploaded!