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The Galerkin continuous finite element method for delay-differential equation with a variable term

APPLIED MATHEMATICS AND COMPUTATION 2007年第2期186卷 1488-1496页

作者： Deng, Kang Xiong, Zhiguang Huang, Yunqing Hunan Univ Sci & Technol Sch Math & Computat Sci Xiangtan 411201 Hunan Peoples R China Xiangtan Univ Sch Math & Computat Sci Xiangtan 411105 Hunan Peoples R China

In this paper, we introduce and analyze the continuous finite element method for a class of delay-differential equation with a variable term. At first for the case of the constant delay and based on an orthogonal expansion in an element we derive optimal superconvergence u - U = O(h(p+2)),p >= 2 at the (p + 1)-order Lobatto points and u - U = O(h(2P)) at the integer nodal points. Next we prove the stability of linear and quadratic finite element schemes for the case of constant delay. For the case of variable delay, by use of the approximative to the continuous delay in every subinterval we decompose the original problem into a series of subproblems with constant delay. Finally we give a recursive schemes which can be compute by every subproblem. (c) 2006 Elsevier Inc. All rights reserved.

关键词： delay-differential equation with a variable term continuous finite element method subproblems with constant superconvergence recursive schemes

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Free surface flows over partially erodible beds by a continuous finite element method

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ENVIRONMENTAL EARTH SCIENCES 2015年第11期74卷 7357-7370页

作者： Ortiz, Pablo Anguita, Javier Riveiro, Miguel Univ Granada Esc Ingn Caminos E-18071 Granada Spain

This paper presents a continuous finite element model for shallow water equations coupled with a bedload sediment conservation law. The model incorporates a sign-preserving conservative correction based on the flux correction transport methodology. Complete algorithm permits simulation of flows with evolutionary boundaries and erodible-non erodible interfaces under severe conditions without spurious mass exchanges and oscillations. Numerical experiments explore the efficacy of the procedure for dam-break problems on channels with dry beds, for partially and totally erodible beds, and for migration of small bedforms. Computation of real river morphodynamics under intense flooding illustrates practical application of the model.

关键词： Evolutionary interfaces Coupled erodible beds Positive algorithm continuous finite element method

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A new and simple implementation of the element-local L²-projected continuous finite element method

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APPLIED MATHEMATICS AND COMPUTATION 2014年 228卷 170-183页

作者： Xue, Yunhua Duan, Huoyuan Zhang, Qiang Nankai Univ Sch Math Sci Tianjin 300071 Peoples R China Nanjing Univ Dept Math Nanjing 210093 Jiangsu Peoples R China

In this paper we present a new and simple method, modified from the original element-local L-2-projected continuous finite element method, to resolve some static electromagnetic problems in two dimension. This numerical method is established on the least-square process to minimize the total error's energy, where the residual due to an additional element-local projection is considered. Many numerical experiments are presented for the electrostatic problem, the Maxwell's equations and the Maxwell's eigenvalue problem, and the numerical performances are excellent with the optimal convergence orders even for the non-H-1 solution. (C) 2013 Elsevier Inc. All rights reserved.

关键词： element-local L-2-projection continuous finite element method Electrostatic problem Maxwell's equations Maxwell's eigenvalues

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A new continuous finite element SN method for solving first-order neutron transport equation

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ANNALS OF NUCLEAR ENERGY 2022年 175卷

作者： Guo, Hewei Chen, Wei Jiang, Xinbiao Jiang, Duoyu Zhang, Xinyi Xi An Jiao Tong Univ Sch Nucl Sci & Technoloy Xian 710049 Shaanxi Peoples R China Northwest Inst Nucl Technol Xian 710024 Peoples R China

A continuous finite element method (FEM) based on B-spline wavelet on the interval (BSWI) is proposed to solve the first-order neutron transport equation with discrete ordinate (SN) angular discretization. Two technologies are applied in this method, one of technologies is that the streamline upwind Petrov-Galerkin (SUPG) method is utilized to stabilize the first-order neutron transport equation when the FEM is used. Another is that the scaling functions of BSWI are applied to replace the usual Lagrange basis function. Based on the above two technologies, the stabilized weak form of neutron transport equation applying the SUPG technology based on BSWI is derived. Finally, some numerical examples are utilized to verify the proposed method. The results demonstrate that the method can treat the void region prob-lem, and compared the FEM with SUPG technology, it can obtain fast convergence and numerical preci-sion under the condition of much less grid. Overall, this method has good accuracy, high computational efficiency and wide application. (c) 2022 Published by Elsevier Ltd.

关键词： B-spline wavelet on the interval continuous finite element method Neutron transport equation Basis function

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线性哈密尔顿系统的m次连续有限元法

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高等学校计算数学学报 2011年第4期33卷 295-311页

作者：汤琼陈传淼刘罗华曹红萍湖南工业大学理学院湖南师范大学数学与计算机科学学院上海工程技术大学管理学院

1引言哈密尔顿系统是一个重要的动力系统,因此如何正确计算哈密尔顿系统有着重要的意义.正确的计算方法离散后应该保持着问题原型的基本特征.其中辛性质和能量守恒是哈密尔顿系统的两个重要特征.冯康和他的研究小组提出了哈密尔顿系统... 详细信息

1引言哈密尔顿系统是一个重要的动力系统,因此如何正确计算哈密尔顿系统有着重要的意义.正确的计算方法离散后应该保持着问题原型的基本特征.其中辛性质和能量守恒是哈密尔顿系统的两个重要特征.冯康和他的研究小组提出了哈密尔顿系统辛几何算法,

关键词： Hamilton equation continuous finite element method symplectic algorithm energy conservation

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CONVERGENCE OF A HOMOTOPY finite element method FOR COMPUTING STEADY STATES OF BURGERS' EQUATION

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ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS-MODELISATION MATHEMATIQUE ET ANALYSE NUMERIQUE 2019年第5期53卷 1629-1644页

作者： Hao, Wenrui Yang, Yong Penn State Univ Dept Math University Pk PA 16802 USA

In this paper, the convergence of a homotopy method (1.1) for solving the steady state problem of Burgers' equation is considered. When nu is fixed, we prove that the solution of (1.1) converges to the unique steady state solution as epsilon -> 0, which is independent of the initial conditions. Numerical examples are presented to confirm this conclusion by using the continuous finite element method. In contrast, when nu = epsilon -> 0, numerically we show that steady state solutions obtained by (1.1) indeed depend on initial conditions.

关键词： Homotopy method continuous finite element method Burgers' equation

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NON-OSCILLATORY FEM FOR FLOWS OVER FLOODING AREAS AND PARTIALLY ERODIBLE BEDS 11

NON-OSCILLATORY FEM FOR FLOWS OVER FLOODING AREAS AND PARTIA...

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11th World Congress on Computational Mechanics (WCCM) / 5th European Conference on Computational Mechanics (ECCM) / 6th European Conference on Computational Fluid Dynamics (ECFD)

作者： Ortiz, Pablo Gomez, Jose Anguita, Javier Univ Granada Campus Fuentenueva E-18071 Granada Spain

ISBN: (纸本)9788494284472

The paper introduces a positive continuous finite element method (FEM) for coupled transport equations, incorporating the shallow water equations and a sediment transport equation. Transport equation relates position of the bed-fluid interface to the divergence of sediment fluxes. The equation is casted as a standard advection-diffusion PDE suitable for an efficient positive-definite continuous FEM model. The continuous FEM is developed by integrating a high order finite element procedure with a conservative flux-correction that imposes sign-preservation, permitting simulation of flows with dry fronts without spurious mass exchanges and oscillations, as well as simulation of the evolution of layers of erodible sediment over partially non-erodible stratums. Experiments focus on applications of the model to the simulation of real river dynamics and evolution of sediment layers with partially non-erodible beds.

关键词： Evolutionary coastlines Coupled erodible beds Positive algorithm continuous finite element method

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An Arbitrary-Lagrangian-Eulerian hybrid finite volume/finite element method on moving unstructured meshes for the Navier-Stokes equations

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APPLIED MATHEMATICS AND COMPUTATION 2023年 437卷

作者： Busto, S. Dumbser, M. Rio-Martin, L. Univ Trento Lab Appl Math DICAM Via Mesiano 77 I-38123 Trento Italy Univ Vigo Dept Matemat Aplicada 1 Campus Lagoas Marcosende S-N Vigo 36310 Spain Univ A Coruna Dept Matemat Campus Elvina S-N La Coruna 15071 Spain

This paper presents a novel semi-implicit hybrid finite volume / finite element (FV/FE) scheme for the numerical solution of the incompressible and weakly compressible Navier-Stokes equations on moving unstructured meshes using a direct Arbitrary-Lagrangian-Eulerian (ALE) formulation. The scheme is based on a suitable splitting of the governing partial differential equations into subsystems and employs a staggered grid arrangement, where the pressure is defined on the primal simplex mesh, while the velocity and the remaining flow quantities are defined on an edge-based staggered dual mesh. The key idea of the scheme presented in this paper is to discretize the nonlinear convective and viscous terms at the aid of an explicit finite volume scheme that employs the space-time divergence form of the governing equations on moving space-time control volumes. For the convective terms, an ALE extension of the Ducros flux on moving meshes is introduced, which can be proven to be kinetic energy preserving and stable in the energy norm when adding suitable numerical dissipation terms. The use of closed space-time control volumes inside the finite volume scheme guarantees that the important geometric conservation law (GCL) of Lagrangian schemes is verified by construction . Finally, the pressure equation of the Navier-Stokes system is solved on the new mesh configuration at the aid of a classical continuous finite element method, using traditional P-1 Lagrange elements. A numerical convergence study confirms that the scheme is second order accurate in space. Subsequently, the ALE hybrid FV/FE method is applied to several incompressible test problems ranging from non-hydrostatic free surface flows over a rising bubble to flows over an oscillating cylinder and an oscillating ellipse. Via the simulation of a circular explosion problem on a moving mesh, we show that the scheme applied to the weakly com-pressible Navier-Stokes equations is able to capture also weak shock waves, raref

关键词： Projection method for the Navier-Stokes equations Staggered semi -implicit schemes Kinetic energy preserving finite volume method continuous finite element method Arbitrary-Lagrangian-Eulerian (ALE) method Space-time control volumes and geometric conservation law (GCL)

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Enhancing the fiber-based modeling approach for flexure-shear behavior in seismic evaluation of long-span railway masonry arch bridges

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ENGINEERING STRUCTURES 2024年 301卷

作者： Heidari, Amirhossein Khanmohammadi, Mohammad Univ Tehran Coll Engn Sch Civil Engn Tehran Iran

Masonry arch bridges are considered a significant part of the rail and road transportation infrastructures in many countries, and seismic assessment of these structures is of great importance for increasing their resilience. Despite some shortcomings in comparison to more complicated modeling techniques, i.e. continuous and discrete techniques, one-dimensional continuous modeling approaches such as the fiber beam approach are more practical for engineering purposes. Although the fiber models can acceptably predict the axial and flexural behavior of structural members, shear or flexure-shear failure behavior, which could be one of the dominant failure modes in masonry structures, cannot be predicted appropriately in this approach. The purpose of this article is to enhance fiber-based modeling approach to consider these brittle failure modes for the seismic assessments of long-span masonry arch bridges. Using the existing analytical-empirical prediction equations reported on the results of stone masonry walls, an iterative approach is proposed to enhance fiber-based model to include flexureshear interaction. the proposed method is verified with a series of arch samples with different geometric properties with results from discontinuous models of the sample arches. Following that, different models of a span of a case-study masonry arch bridge is created, verified with health monitoring field observation, and analyzed to compare from different aspects and validate the application of the fiber beam method along with its enhancements. The results of the proposed method for fiber models show promising conformity with the results of more precise numerical models, and it can be used for the seismic evaluation of long-span stone masonry bridges.

关键词： Masonry arch bridge Fiber -beam model continuous finite element method Discrete element method Shear failure Flexure -Shear interaction

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