High-order implicit palindromic discontinuous Galerkin method for kinetic-relaxation approximation

回文间断有限元方法用于具有刚性松弛的动能方程

Palindromic discontinuous Galerkin method for kinetic equations with stiff relaxation

本文提出一种高阶方案，用于近似具有刚性松弛的动能方程，通过高阶隐式迎风间断有限元方法、基于对称性的二级渐近无损时间积分以及回文组合实现更高阶时间精度。

Discontinuous Galerkin approximations for an optimal control problem of three-dimensional Navier-Stokes-Voigt equations

We analyze a fully discrete scheme based on the discontinuous (in time) Galerkin approach, which is combined with conforming finite element subspaces in space, for the distributed optimal control problem of the three-dimensional Navier-Stokes-Voigt equations with a quadratic objective functional and box control constraints. The space-time error estimates of order $O(\sqrtτ+h)$, where $τ$ and $h$ are respectively the time and space discretization parameters, are proved for the difference between the locally optimal controls and their discrete approximations.

基于间断伽辽金技术的反应扩散问题新变分公式

A new variational formulation based on discontinuous Galerkin technique for a reaction-diffusion problem

提出一种基于间断伽辽金技术的反应扩散问题新变分公式，证明其适定性，并指出该公式有助于设计在空间变量上强稳定、时间变量上绝对稳定且最优收敛的混合数值方法。

Stabilizing discontinuous Galerkin methods using Dafermos' entropy rate criterion

A novel approach for the stabilization of the discontinuous Galerkin method based on the Dafermos entropy rate crition is presented. The approach is centered around the efficient solution of linear or nonlinear optimization problems in every timestep as a correction to the basic discontinuous Galerkin scheme. The thereby enforced Dafermos criterion results in improved stability compared to the basic method while retaining the order of the method in numerical experiments. Further modification of the optimization problem allows also to enforce classical entropy inequalities for the scheme. The p…

First-order continuous- and discontinuous-Galerkin moment models for a linear kinetic equation: model derivation and realizability theory

We provide two new classes of moment models for linear kinetic equations in slab and three-dimensional geometry. They are based on classical finite elements and low-order discontinuous-Galerkin approximations on the unit sphere. We investigate their realizability conditions and other basic properties. Numerical tests show that these models are more efficient than classical full-moment models in a space-homogeneous test, when the analytical solution is not smooth.

Unified Analysis of Discontinuous Galerkin Methods for Frictional Contact Problem with normal compliance

In this article, a reliable and efficient a posteriori error estimator of residual type is derived for a class of discontinuous Galerkin methods for the frictional contact problem with reduced normal compliance which is modeled as a quasi-variational inequality. We further derive a priori error estimates in the energy norm under the minimal regularity assumption on the exact solution. The convergence behavior of error over uniform mesh and the performance of error estimator are illustrated by the numerical results.