In this paper, a method to develop a hierarchy of explicit recursion formulas for numerical simulation in an irregular grid for scalar wave equations is presented and its accuracy is illustrated via 2-D and 1-D models...In this paper, a method to develop a hierarchy of explicit recursion formulas for numerical simulation in an irregular grid for scalar wave equations is presented and its accuracy is illustrated via 2-D and 1-D models. Approaches to develop the stable formulas which are of 2M-order accuracy in both time and space with Mbeing a positive integer for regular grids are discussed and illustrated by constructing the second order （M= 1） and the fourth order （M = 2） recursion formulas.展开更多
The purpose of this article is to develop and analyze least-squares approximations for the incompressible magnetohydrodynamic equations. The major advantage of the least-squares finite element method is that it is not...The purpose of this article is to develop and analyze least-squares approximations for the incompressible magnetohydrodynamic equations. The major advantage of the least-squares finite element method is that it is not subjected to the so-called Ladyzhenskaya-Babuska-Brezzi （LBB） condition. The authors employ least-squares functionals which involve a discrete inner product which is related to the inner product in H^-1（Ω）.展开更多
In this paper, an explicit method is generalized from 1D and 2D models to a 3D model for numerical simulation of wave motion, and the corresponding recursion formulas are developed for 3D irregular grids. For uniform ...In this paper, an explicit method is generalized from 1D and 2D models to a 3D model for numerical simulation of wave motion, and the corresponding recursion formulas are developed for 3D irregular grids. For uniform cubic grids, the approach used to establish stable formulas with 2M-order accuracy is discussed in detail, with M being a positive integer, and is illustrated by establishing second order （M=1） recursion formulas. The theoretical results presented in this paper are demonstrated through numerical testing.展开更多
Blade clearance is an important technical parameter of the shear, which determines the shear quality of plate. The finite element method was used to simulate shearing process which is in the different specifications a...Blade clearance is an important technical parameter of the shear, which determines the shear quality of plate. The finite element method was used to simulate shearing process which is in the different specifications and blade clearances, and the impact on blade section and shearing force of blade clearance was analyzed. Comparing with traditional experience formulas and measured values, the limitations of the experience formulas were proved. And by contrasting with the shearing force data collected from Linfen Iron and Steel Company, the reliability of the finite element method was further proved. The simulated results show that the simulated values controlled by ductile fracture criterion and measured values are very close, and the deviation value is in the range of 4.8%-20.8%. For the same steel, if the plate is thicker, the blade clearance will be greater, and thickness and blade clearance are approximately linear. The difference between numerical simulation of the maximum shearing force and the measured results is 7.7% to 12.0%, and the simulation results are close to facts. With the increase of blade clearance and the thickness, the shearing force was increased to some degree.展开更多
This article concerns numerical approximation of a parabolic interface problem with general L 2 initial value.The problem is discretized by a finite element method with a quasi-uniform triangulation of the domain fitt...This article concerns numerical approximation of a parabolic interface problem with general L 2 initial value.The problem is discretized by a finite element method with a quasi-uniform triangulation of the domain fitting the interface,with piecewise linear approximation to the interface.The semi-discrete finite element problem is furthermore discretized in time by the k-step backward difference formula with k=1,...,6.To maintain high-order convergence in time for possibly nonsmooth L 2 initial value,we modify the standard backward difference formula at the first k−1 time levels by using a method recently developed for fractional evolution equations.An error bound of O(t−k nτk+t−1 n h 2|log h|)is established for the fully discrete finite element method for general L 2 initial data.展开更多
In this paper,we study the finite element approximation for nonlinear thermal equation.Because the nonlinearity of the equation,our theoretical analysis is based on the error of temporal and spatial discretization.We ...In this paper,we study the finite element approximation for nonlinear thermal equation.Because the nonlinearity of the equation,our theoretical analysis is based on the error of temporal and spatial discretization.We consider a fully discrete second order backward difference formula based on a finite element method to approximate the temperature and electric potential,and establish optimal L^(2) error estimates for the fully discrete finite element solution without any restriction on the time-step size.The discrete solution is bounded in infinite norm.Finally,several numerical examples are presented to demonstrate the accuracy and efficiency of the proposed method.展开更多
基金National Basic Research Program of China Under Grant No. 2007CB714200National Natural Science Foundation of China Under Grant No. 90715038
文摘In this paper, a method to develop a hierarchy of explicit recursion formulas for numerical simulation in an irregular grid for scalar wave equations is presented and its accuracy is illustrated via 2-D and 1-D models. Approaches to develop the stable formulas which are of 2M-order accuracy in both time and space with Mbeing a positive integer for regular grids are discussed and illustrated by constructing the second order （M= 1） and the fourth order （M = 2） recursion formulas.
基金supported by the National Basic Research Program of China (2005CB321701)NSF of mathematics research special fund of Hebei Province(08M005)
文摘The purpose of this article is to develop and analyze least-squares approximations for the incompressible magnetohydrodynamic equations. The major advantage of the least-squares finite element method is that it is not subjected to the so-called Ladyzhenskaya-Babuska-Brezzi （LBB） condition. The authors employ least-squares functionals which involve a discrete inner product which is related to the inner product in H^-1（Ω）.
基金China Postdoctoral Science Foundation Under Grant No.20100480321National Basic Research Program of China Under Grant No. 2007CB714200
文摘In this paper, an explicit method is generalized from 1D and 2D models to a 3D model for numerical simulation of wave motion, and the corresponding recursion formulas are developed for 3D irregular grids. For uniform cubic grids, the approach used to establish stable formulas with 2M-order accuracy is discussed in detail, with M being a positive integer, and is illustrated by establishing second order （M=1） recursion formulas. The theoretical results presented in this paper are demonstrated through numerical testing.
基金Item Sponsored by National Key Basic Research Program of China (2012CB722801)
文摘Blade clearance is an important technical parameter of the shear, which determines the shear quality of plate. The finite element method was used to simulate shearing process which is in the different specifications and blade clearances, and the impact on blade section and shearing force of blade clearance was analyzed. Comparing with traditional experience formulas and measured values, the limitations of the experience formulas were proved. And by contrasting with the shearing force data collected from Linfen Iron and Steel Company, the reliability of the finite element method was further proved. The simulated results show that the simulated values controlled by ductile fracture criterion and measured values are very close, and the deviation value is in the range of 4.8%-20.8%. For the same steel, if the plate is thicker, the blade clearance will be greater, and thickness and blade clearance are approximately linear. The difference between numerical simulation of the maximum shearing force and the measured results is 7.7% to 12.0%, and the simulation results are close to facts. With the increase of blade clearance and the thickness, the shearing force was increased to some degree.
文摘This article concerns numerical approximation of a parabolic interface problem with general L 2 initial value.The problem is discretized by a finite element method with a quasi-uniform triangulation of the domain fitting the interface,with piecewise linear approximation to the interface.The semi-discrete finite element problem is furthermore discretized in time by the k-step backward difference formula with k=1,...,6.To maintain high-order convergence in time for possibly nonsmooth L 2 initial value,we modify the standard backward difference formula at the first k−1 time levels by using a method recently developed for fractional evolution equations.An error bound of O(t−k nτk+t−1 n h 2|log h|)is established for the fully discrete finite element method for general L 2 initial data.
文摘In this paper,we study the finite element approximation for nonlinear thermal equation.Because the nonlinearity of the equation,our theoretical analysis is based on the error of temporal and spatial discretization.We consider a fully discrete second order backward difference formula based on a finite element method to approximate the temperature and electric potential,and establish optimal L^(2) error estimates for the fully discrete finite element solution without any restriction on the time-step size.The discrete solution is bounded in infinite norm.Finally,several numerical examples are presented to demonstrate the accuracy and efficiency of the proposed method.
