Blast Damage Simulation With the Discontinuous Galerkin Finite Element Method of Bond⁃Based Peridynamics北大核心CSCD

近场动力学是一种积分型非局部的连续介质力学理论,已广泛应用于固体材料和结构的非连续变形与破坏分析中,其数值求解方法主要采用无网格粒子类的显式动力学方法.近年来,弱形式近场动力学方程的非连续Galerkin有限元法得到发展,该方法不仅可以描述考察体的非局部作用效应和非连续变形特性,还可以充分利用有限单元法高效求解的特点,并继承了有限元法能直接施加局部边界条件的优点,可有效避免近场动力学的表面效应问题.该文阐述了键型近场动力学的非连续Galerkin有限元法的基本原理,导出了计算列式,给出了具体算法流程和细节,计算模拟了脆性玻璃板动态开裂分叉问题,并对爆炸冲击荷载作用下混凝土板的毁伤过程进行了计算分析.研究结果表明,该方法能够再现爆炸冲击荷载作用下结构的复杂破裂模式和毁伤破坏过程,且具有较高的计算效率,是模拟结构爆炸冲击毁伤效应的一种有效方法.     

Optimal L ∞-Error Estimate of a Finite Element Method for Hamilton–Jacobi–Bellman Equations

This paper is concerned with the piecewise linear finite element approximation of Hamilton–Jacobi–Bellman equations. We establish the optimal L ^∞-error estimate, combining the concepts of subsolution and discrete regularity.     

Summarizing an Eulerian–Lagrangian model for subsea gas release and comparing release of CO2 with CH4

A subsea gas release is a concern for both safety and environment. This can be assessed by mathematical models. The development of an Eulerian–Lagrangian modelling concept to study subsea gas release has taken place over many years and the piecewise enhancements have been documented in the open literature. The model in its current state is summarized in this article. Model simulations are shown to be consistent with different experiments varying in depth from 7 to 138 m. The model can be applied to estimate how gas surfaces into the atmosphere from a subsea source. This is vital input to risk assessments. Due to recent interest in subsea CO₂ storage and transport, a comparison of CO₂- and CH₄-releases has been performed. Model results show that a much smaller fraction of released CO₂ reaches the atmosphere than CH₄ due to the high solubility of CO₂ in water.     

Hierarchical Elements,Local Mappings and the $h$-$p$ Version of the Finite Element Method (Ⅰ)

This is the first half of an article which develops a theory the hierarchical elements for the $h$-$p$ version of the finite element method in the two-dimensional case. The approximation properties of the hierarchical elements are discussed. The second part will address the convergence rate when geometric meshes are used.     

Hierarchical Elements,Local Mappings and the $H$-$P$ Version of the Finite Element Method (Ⅱ)

This is the second half of the article. The rate of convergence for the $h$-$p$ version with geometric meshes is discussed.     

Convergence of Adaptive Discontinuous Galerkin and $$C^0$$ -Interior Penalty Finite Element Methods for Hamilton–Jacobi–Bellman and Isaacs Equations

Foundations of Computational Mathematics - We prove the convergence of adaptive discontinuous Galerkin and $$C^0$$ -interior penalty methods for fully nonlinear second-order elliptic...     

Convergence Analysis of the Nonconforming Finite Element Discretization of Stokes and Navier–Stokes Equations with Nonlinear Slip Boundary Conditions

This work is concerned with the nonconforming finite approximations for the Stokes and Navier–Stokes equations driven by slip boundary condition of “friction” type. It is well documented that if the velocity is approximated by the Crouzeix–Raviart element of order one, whereas the discrete pressure is constant elementwise that the inequality of Korn does not hold. Hence, we propose a new formulation taking into account the curvature and the contribution of tangential velocity at the boundary. Using the maximal regularity of the weak solution, we derive a priori error estimates for the velocity and pressure by taking advantage of the enrichment mapping and the application of Babuska–Brezzi’s theory for mixed problems.     

Development and Application of an Exponential Method for Integrating Stiff Systems Based on the Classical Runge–Kutta Method

We study numerical methods for solving stiff systems of ordinary differential equations. We propose an exponential computational algorithm which is constructed by using an exponential change of variables based on the classical Runge–Kutta method of the fourth order. Nonlinear problems are used to prove and demonstrate the fourth order of convergence of the new method.