Asymptotic error expansions in H^1-norm for the bilinear finite element approximation to a class of optimal control problems are derived for rectangular meshes. With the rectan- gular meshes, the Richardson extrapolat...Asymptotic error expansions in H^1-norm for the bilinear finite element approximation to a class of optimal control problems are derived for rectangular meshes. With the rectan- gular meshes, the Richardson extrapolation of two different schemes and an interpolation defect correction can be applied. The higher order numerical approximations are used to generate a posteriori error estimators for the finite element approximation.展开更多
利用大型有限元分析软件ANSYS分析了国际热核实验反应堆(ITER)Side校正场线圈(CC)端部三维大圆弧模压成形及释放模具后导体的回弹效应,研究了不同半径成形时导体内外表面的应力、应变的分布及释放模具后导体的回弹规律。设计了1套模压...利用大型有限元分析软件ANSYS分析了国际热核实验反应堆(ITER)Side校正场线圈(CC)端部三维大圆弧模压成形及释放模具后导体的回弹效应,研究了不同半径成形时导体内外表面的应力、应变的分布及释放模具后导体的回弹规律。设计了1套模压成形模具,通过修模的方式在该套成形模具上进行了不同半径成形试验,测得了不同成形半径时模压成形后的回弹量值。试验结果验证了所建立的有限元分析模型的正确性。有限元分析和试验结果表明:ITERSideCC端部三维大圆弧可通过模压成形达到所需的大半径要求,为ITER Side CC端部三维大圆弧成形提供了一种可行方案。展开更多
In this paper, the Wilson nonconforming finite element is considered for solving a class of second-order elliptic boundary value problems. Based on an asymptotic error expansion for the Wilson finite element, the glob...In this paper, the Wilson nonconforming finite element is considered for solving a class of second-order elliptic boundary value problems. Based on an asymptotic error expansion for the Wilson finite element, the global superconvergences, the local superconvergences and the defect correction schemes are presented.展开更多
In this paper, a semi-discrete defect-correction mixed finite element method (MFEM) for solving the non-stationary conduction-convection problems in two dimension is presented. In this method, we solve the nonlinear e...In this paper, a semi-discrete defect-correction mixed finite element method (MFEM) for solving the non-stationary conduction-convection problems in two dimension is presented. In this method, we solve the nonlinear equations with an added artificial viscosity term on a finite element grid and correct this solutions on the same grid using a linearized defect-correction technique. The stability and the error analysis are derived. The theory analysis shows that our method is stable and has a good convergence property.展开更多
In this paper, by combining the second order characteristics time discretization with the variational multiscale finite element method in space we get a second order modified characteristics variational multiscale fin...In this paper, by combining the second order characteristics time discretization with the variational multiscale finite element method in space we get a second order modified characteristics variational multiscale finite element method for the time dependent Navier- Stokes problem. The theoretical analysis shows that the proposed method has a good convergence property. To show the efficiency of the proposed finite element method, we first present some numerical results for analytical solution problems. We then give some numerical results for the lid-driven cavity flow with Re = 5000, 7500 and 10000. We present the numerical results as the time are sufficient long, so that the steady state numerical solutions can be obtained.展开更多
In this paper, the error of the following defect correction process are discussed.where uh E S1h is the linear finite element solution and S. Under natu-ral smoothness assumption, it is proved that the correction solu...In this paper, the error of the following defect correction process are discussed.where uh E S1h is the linear finite element solution and S. Under natu-ral smoothness assumption, it is proved that the correction solution I2uhincreases the accuracy for the Uh.展开更多
基金supported in part by the National Basic Research Program (2007CB814906)the National Natural Science Foundation of China (10471103 and 10771158)+4 种基金Social Science Foundation of the Ministry of Education of China (06JA630047)Tianjin Natural Science Foundation (07JCYBJC14300)Tianjin University of Finance and Economicssupported by the National Basic Research Program under the Grant 2005CB321701the National Natural Science Foundation of China under the Grant 10771211
文摘Asymptotic error expansions in H^1-norm for the bilinear finite element approximation to a class of optimal control problems are derived for rectangular meshes. With the rectan- gular meshes, the Richardson extrapolation of two different schemes and an interpolation defect correction can be applied. The higher order numerical approximations are used to generate a posteriori error estimators for the finite element approximation.
文摘利用大型有限元分析软件ANSYS分析了国际热核实验反应堆(ITER)Side校正场线圈(CC)端部三维大圆弧模压成形及释放模具后导体的回弹效应,研究了不同半径成形时导体内外表面的应力、应变的分布及释放模具后导体的回弹规律。设计了1套模压成形模具,通过修模的方式在该套成形模具上进行了不同半径成形试验,测得了不同成形半径时模压成形后的回弹量值。试验结果验证了所建立的有限元分析模型的正确性。有限元分析和试验结果表明:ITERSideCC端部三维大圆弧可通过模压成形达到所需的大半径要求,为ITER Side CC端部三维大圆弧成形提供了一种可行方案。
基金The National Natural Science Foundation of China(1117126911401074)+8 种基金the Ph.D.Program Foundation of Ministry of Education of China(20110201110027)the China Postdoctoral Science Foundation(2013M531311)the Research Fund of Educational Commission of Henan Province of China(14B11002014B11002114B110025)the Henan Scienti?c and Technological Research Project(132102310309)the Doctoral Foundation of Henan University of Science and Technology(09001625)the Science Foundation for Cultivating Innovation Ability of Henan University of Science and Technology(2014ZCX009)the Youth Scienti?c Foundation of Henan University of Science and Technology(2012QN029)
文摘In this paper, the Wilson nonconforming finite element is considered for solving a class of second-order elliptic boundary value problems. Based on an asymptotic error expansion for the Wilson finite element, the global superconvergences, the local superconvergences and the defect correction schemes are presented.
基金supported by National Natural Science Foundation of China (Grant No.10971166)the National Basic Research Program of China (Grant No. 2005CB321703)
文摘In this paper, a semi-discrete defect-correction mixed finite element method (MFEM) for solving the non-stationary conduction-convection problems in two dimension is presented. In this method, we solve the nonlinear equations with an added artificial viscosity term on a finite element grid and correct this solutions on the same grid using a linearized defect-correction technique. The stability and the error analysis are derived. The theory analysis shows that our method is stable and has a good convergence property.
文摘In this paper, by combining the second order characteristics time discretization with the variational multiscale finite element method in space we get a second order modified characteristics variational multiscale finite element method for the time dependent Navier- Stokes problem. The theoretical analysis shows that the proposed method has a good convergence property. To show the efficiency of the proposed finite element method, we first present some numerical results for analytical solution problems. We then give some numerical results for the lid-driven cavity flow with Re = 5000, 7500 and 10000. We present the numerical results as the time are sufficient long, so that the steady state numerical solutions can be obtained.
文摘In this paper, the error of the following defect correction process are discussed.where uh E S1h is the linear finite element solution and S. Under natu-ral smoothness assumption, it is proved that the correction solution I2uhincreases the accuracy for the Uh.
