A two-level algorithm for the weak Galerkin discretization of diffusion problems

This paper analyzes a two-level algorithm for the weak Galerkin (WG) finite element methods based on local Raviart-Thomas (RT) and Brezzi-Douglas-Marini (BDM) mixed elements for two- and three-dimensional diffusion problems with Dirichlet condition. We first show the condition numbers of the stiffness matrices arising from the WG methods are of $O(h^{-2})$. We use an extended version of the Xu-Zikatanov (XZ) identity to derive the convergence of the algorithm without any regularity assumption. Finally we provide some numerical results

Uniformly stable rectangular elements for fourth order elliptic singular perturbation problems

This paper analyzes rectangular finite element methods for fourth order elliptic singular perturbation problems. We show that the non-$C^0$ rectangular Morley element is uniformly convergent in the energy norm with respect to the perturbation parameter. We also propose a $C^0$ extended high order rectangular Morley element and prove the uniform convergence. Finally, we do some numerical experiments to confirm the theoretical results

A Colored Particle Acceleration by Fluctuations in QGP

We discuss the energy variation of a parton passing through a quark-gluon plasma(QGP) taking into account nonlinear polarization effect. We find the parton can be accelerated by fluctuations in QGP, which gives us a new physical insight about the response of QGP to such external the current.Comment: 6 page

Analysis of a family of HDG methods for second order elliptic problems

In this paper, we analyze a family of hybridizable discontinuous Galerkin (HDG) methods for second order elliptic problems in two and three dimensions. The methods use piecewise polynomials of degree $k\geqslant 0$ for both the flux and numerical trace, and piecewise polynomials of degree $k+1$ for the potential. We establish error estimates for the numerical flux and potential under the minimal regularity condition. Moreover, we construct a local postprocessing for the flux, which produces a numerical flux with better conservation. Numerical experiments in two-space dimensions confirm our theoretical results.Comment: 18 page

Covariant Perturbation Theory of Non-Abelian Kinetic Theory

A double perturbation idea is presented in framework of the quark-gluon plasma kinetic theory. A solvable set of equations from the 'double perturbation' is derived and the equations are showed to be gauge-independent. The formalism of Landau damping rate for the plasmon at zero momentum is given and discussed.Comment: 8page

Regularity for time fractional wave problems

Using the Galerkin method, we obtain the unique existence of the weak solution to a time fractional wave problem, and establish some regularity estimates which reveal the singularity structure of the weak solution in time

Regularity of solutions to time fractional diffusion equations

We derive some regularity estimates of the solution to a time fractional diffusion equation, that are useful for numerical analysis, and partially unravel the singularity structure of the solution with respect to the time variable

Explicit calculation of strong solution on linear parabolic equation

In this paper, we give the existence and uniqueness of the strong solution of one dimensional linear parabolic equation with mixed boundary conditions. The boundary conditions can be any kind of mixed Dirichlet, Neumann and Robin boundary conditions. We use the extension method to get the unique solution. Furthermore, the method can also be easily implemented as a numerical method. Some simple examples are presented.Comment: 10 page

Convergence analysis of a Petrov-Galerkin method for fractional wave problems with nonsmooth data

This paper analyzes the convergence of a Petrov-Galerkin method for time fractional wave problems with nonsmooth data. Well-posedness and regularity of the weak solution to the time fractional wave problem are firstly established. Then an optimal convergence analysis with nonsmooth data is derived. Moreover, several numerical experiments are presented to validate the theoretical results

On weaving g-frames for Hilbert spaces

Weaving frames are powerful tools in wireless sensor networks and pre-processing signals. In this paper, we introduce the concept of weaving for g-frames in Hilbert spaces. We first give some properties of weaving g-frames and present two necessary conditions in terms of frame bounds for weaving g-frames. Then we study the properties of weakly woven g-frames and give a sufficient condition for weaving g-frames. It is shown that weakly woven is equivalent to woven. Two sufficient conditions for weaving g-Riesz bases are given. And a weaving equivalent of an unconditional g-basis for weaving g-Riesz bases is considered. Finally, we present Paley-Wiener-type perturbation results for weaving g-frames.Comment: Part of the argument is wrong. arXiv admin note: text overlap with arXiv:1503.03947 by other author