A modified penalty scheme is discussed for solving the Stokes problem with the Crouzeix-Raviart type nonconforming linear triangular finite element. By the L^2 projection method, the superconvergence results for the v...A modified penalty scheme is discussed for solving the Stokes problem with the Crouzeix-Raviart type nonconforming linear triangular finite element. By the L^2 projection method, the superconvergence results for the velocity and pressure are obtained with a penalty parameter larger than that of the classical penalty scheme. The numerical experiments are carried out to confirm the theoretical results.展开更多
Numerical experiments are given to verify the theoretical results for superconvergence of the elliptic problem by global and local L2-Projection methods.
Based on rectangular partition and bilinear interpolation,we construct an alternating-direction implicit(ADI)finite volume element method,which combined the merits of finite volume element method and alternating direc...Based on rectangular partition and bilinear interpolation,we construct an alternating-direction implicit(ADI)finite volume element method,which combined the merits of finite volume element method and alternating direction implicit method to solve a viscous wave equation with variable coefficients.This paper presents a general procedure to construct the alternating-direction implicit finite volume element method and gives computational schemes.Optimal error estimate in L2 norm is obtained for the schemes.Compared with the finite volume element method of the same convergence order,our method is more effective in terms of running time with the increasing of the computing scale.Numerical experiments are presented to show the efficiency of our method and numerical results are provided to support our theoretical analysis.展开更多
The superconvergence in the finite element method is a phenomenon in which the finite element approximation converges to the exact solution at a rate higher than the optimal order error estimate. Wang proposed and ana...The superconvergence in the finite element method is a phenomenon in which the finite element approximation converges to the exact solution at a rate higher than the optimal order error estimate. Wang proposed and analyzed superconvergence of the conforming finite element method by L2-projections. The goal of this paper is to perform numerical experiments using MATLAB to support and to verify the theoretical results in Wang for the superconvergence of the conforming finite element method (CFEM) for the second order elliptic problems by L2-projection methods. MATLAB codes are published at https://github.com/annaleeharris/Superconvergence-CFEM for anyone to use and to study.展开更多
The superconvergence in the finite element method is a phenomenon in which the fi-nite element approximation converges to the exact solution at a rate higher than the optimal order error estimate. Wang proposed and an...The superconvergence in the finite element method is a phenomenon in which the fi-nite element approximation converges to the exact solution at a rate higher than the optimal order error estimate. Wang proposed and analyzed superconvergence of the conforming finite element method by L2-projections. However, since the conforming finite element method (CFEM) requires a strong continuity, it is not easy to construct such finite elements for the complex partial differential equations. Thus, the nonconforming finite element method (NCFEM) is more appealing computationally due to better stability and flexibility properties compared to CFEM. The objective of this paper is to establish a general superconvergence result for the nonconforming finite element approximations for second-order elliptic problems by L2-projection methods by applying the idea presented in Wang. MATLAB codes are published at https://github.com/annaleeharris/Superconvergence-NCFEM for anyone to use and to study. The results of numerical experiments show great promise for the robustness, reliability, flexibility and accuracy of superconvergence in NCFEM by L2- projections.展开更多
The 2D data processing adopted by the high-density resistivity method regards the geological structures as two degrees, which makes the results of the 2D data inversion only an approximate interpretation;the accuracy ...The 2D data processing adopted by the high-density resistivity method regards the geological structures as two degrees, which makes the results of the 2D data inversion only an approximate interpretation;the accuracy and effect can not meet the precise requirement of the inversion. Two typical models of the geological bodies were designed, and forward calculation was carried out using finite element method. The forward-modeled profiles were obtained. 1% Gaussian random error was added in the forward models and then 2D and 3D inversions using a high-density resistivity method were undertaken to realistically simulate field data and analyze the sensitivity of the 2D and 3D inversion algorithms to noise. Contrast between the 2D and 3D inversion results of least squares inversion shows that two inversion results of high-density resistivity method all can basically reflect the spatial position of an anomalous body. However, the 3D inversion can more effectively eliminate the influence of interference from Gaussian random error and better reflect the distribution of resistivity in the anomalous bodies. Overall, the 3D inversion was better than 2D inversion in terms of embodying anomalous body positions, morphology and resistivity properties.展开更多
In order to achieve a modulator with broad bandwidth and perfect impedance match,a novel electro-optical modulator based on GeO2-doped silica waveguides on silicon substrate is designed.The finite element model of the...In order to achieve a modulator with broad bandwidth and perfect impedance match,a novel electro-optical modulator based on GeO2-doped silica waveguides on silicon substrate is designed.The finite element model of the whole electro-optical modulator is established by means of ANSYS.With the finite element method analysis,the performance of the novel modulator is predicted.The simulation reveals that the designed modulator operates with a product of 3 dB optical bandwidth and modulating length of 226.59 GHz·cm,and a characteristic impedance of 51.6 Ω at 1 550 nm wavelength.Moreover,the calculated electrical reflected power of coplanar waveguide electrode is below-20 dB in the frequency ranging from 45 MHz to 65 GHz.Therefore,the designed modulator has wide modulation bandwidth and perfect impedance match.展开更多
This article discusses the enhanced oil recovery numerical simulation of the chemical flooding(such as surfactants, alcohol, polymers) composed of two-dimensional multicomponent, ultiphase and incompressible mixed flu...This article discusses the enhanced oil recovery numerical simulation of the chemical flooding(such as surfactants, alcohol, polymers) composed of two-dimensional multicomponent, ultiphase and incompressible mixed fluids. After the oil field is waterflooded, there is still a large amount of crude oil left in the oil deposit. By adding certain chemical substances to the fluid injected, its driving capacity can be greatly increased. The mathematical model of two-dimensional enhanced oil recovery simulation can be described展开更多
In this paper we propose a characteristics mixed finite element method to overcome thenumerical dispersion for the 2-phase immiscible displacement. The pressure and associatedfluid velocity will be approximated by a m...In this paper we propose a characteristics mixed finite element method to overcome thenumerical dispersion for the 2-phase immiscible displacement. The pressure and associatedfluid velocity will be approximated by a mixed finite element method, and the saturationwill be treated by a backward characteristics method. The L_∞ stability and convergence forthe scheme are proved, and optimal-order error estimates in L_∞ are obtained.展开更多
Although SnO_2-based nanomaterials used to be considered as being extraordinarily versatile for application to nanosensors,microelectronic devices, lithium-ion batteries, supercapacitors and other devices, the functio...Although SnO_2-based nanomaterials used to be considered as being extraordinarily versatile for application to nanosensors,microelectronic devices, lithium-ion batteries, supercapacitors and other devices, the functionalities of SnO_2-based nanomaterials are severely limited by their intrinsic vulnerabilities. Facile electrospinning was used to prepare SnO_2 nanofibers coated with a protective carbon layer. The mechanical properties of individual core-shell-structured SnO_2@C nanofibers were investigated by atomic force microscopy and the finite element method. The elastic moduli of the carbon-coated SnO_2 nanofibers remarkably increased, suggesting that coating SnO_2 nanofibers with carbon could be an effective method of improving their mechanical properties.展开更多
基金supported by the National Natural Science Foundation of China (Nos. 10971203 and 11271340)the Research Fund for the Doctoral Program of Higher Education of China (No. 20094101110006)
文摘A modified penalty scheme is discussed for solving the Stokes problem with the Crouzeix-Raviart type nonconforming linear triangular finite element. By the L^2 projection method, the superconvergence results for the velocity and pressure are obtained with a penalty parameter larger than that of the classical penalty scheme. The numerical experiments are carried out to confirm the theoretical results.
文摘Numerical experiments are given to verify the theoretical results for superconvergence of the elliptic problem by global and local L2-Projection methods.
基金supported by the National Natural Science Foundation of China grants No.11971241.
文摘Based on rectangular partition and bilinear interpolation,we construct an alternating-direction implicit(ADI)finite volume element method,which combined the merits of finite volume element method and alternating direction implicit method to solve a viscous wave equation with variable coefficients.This paper presents a general procedure to construct the alternating-direction implicit finite volume element method and gives computational schemes.Optimal error estimate in L2 norm is obtained for the schemes.Compared with the finite volume element method of the same convergence order,our method is more effective in terms of running time with the increasing of the computing scale.Numerical experiments are presented to show the efficiency of our method and numerical results are provided to support our theoretical analysis.
文摘The superconvergence in the finite element method is a phenomenon in which the finite element approximation converges to the exact solution at a rate higher than the optimal order error estimate. Wang proposed and analyzed superconvergence of the conforming finite element method by L2-projections. The goal of this paper is to perform numerical experiments using MATLAB to support and to verify the theoretical results in Wang for the superconvergence of the conforming finite element method (CFEM) for the second order elliptic problems by L2-projection methods. MATLAB codes are published at https://github.com/annaleeharris/Superconvergence-CFEM for anyone to use and to study.
文摘The superconvergence in the finite element method is a phenomenon in which the fi-nite element approximation converges to the exact solution at a rate higher than the optimal order error estimate. Wang proposed and analyzed superconvergence of the conforming finite element method by L2-projections. However, since the conforming finite element method (CFEM) requires a strong continuity, it is not easy to construct such finite elements for the complex partial differential equations. Thus, the nonconforming finite element method (NCFEM) is more appealing computationally due to better stability and flexibility properties compared to CFEM. The objective of this paper is to establish a general superconvergence result for the nonconforming finite element approximations for second-order elliptic problems by L2-projection methods by applying the idea presented in Wang. MATLAB codes are published at https://github.com/annaleeharris/Superconvergence-NCFEM for anyone to use and to study. The results of numerical experiments show great promise for the robustness, reliability, flexibility and accuracy of superconvergence in NCFEM by L2- projections.
基金Projects(41074085,41374118)supported by the National Natural Science Foundation of ChinaProject(20120162110015)supported by Doctoral Fund of Ministry of Education of ChinaProject(NCET-12-0551)supported by Program for New Century Excellent Talents in University,China
文摘The 2D data processing adopted by the high-density resistivity method regards the geological structures as two degrees, which makes the results of the 2D data inversion only an approximate interpretation;the accuracy and effect can not meet the precise requirement of the inversion. Two typical models of the geological bodies were designed, and forward calculation was carried out using finite element method. The forward-modeled profiles were obtained. 1% Gaussian random error was added in the forward models and then 2D and 3D inversions using a high-density resistivity method were undertaken to realistically simulate field data and analyze the sensitivity of the 2D and 3D inversion algorithms to noise. Contrast between the 2D and 3D inversion results of least squares inversion shows that two inversion results of high-density resistivity method all can basically reflect the spatial position of an anomalous body. However, the 3D inversion can more effectively eliminate the influence of interference from Gaussian random error and better reflect the distribution of resistivity in the anomalous bodies. Overall, the 3D inversion was better than 2D inversion in terms of embodying anomalous body positions, morphology and resistivity properties.
基金Supported by National Natural Science Foundation of China (No.60577023)Key Laboratory of Opto-Electronics Information and Technical Science of Ministry of Education,China
文摘In order to achieve a modulator with broad bandwidth and perfect impedance match,a novel electro-optical modulator based on GeO2-doped silica waveguides on silicon substrate is designed.The finite element model of the whole electro-optical modulator is established by means of ANSYS.With the finite element method analysis,the performance of the novel modulator is predicted.The simulation reveals that the designed modulator operates with a product of 3 dB optical bandwidth and modulating length of 226.59 GHz·cm,and a characteristic impedance of 51.6 Ω at 1 550 nm wavelength.Moreover,the calculated electrical reflected power of coplanar waveguide electrode is below-20 dB in the frequency ranging from 45 MHz to 65 GHz.Therefore,the designed modulator has wide modulation bandwidth and perfect impedance match.
基金This project is sponsored by the National Scaling Programthe National Eighth-Five-Year Tackling Key Problems Program
文摘This article discusses the enhanced oil recovery numerical simulation of the chemical flooding(such as surfactants, alcohol, polymers) composed of two-dimensional multicomponent, ultiphase and incompressible mixed fluids. After the oil field is waterflooded, there is still a large amount of crude oil left in the oil deposit. By adding certain chemical substances to the fluid injected, its driving capacity can be greatly increased. The mathematical model of two-dimensional enhanced oil recovery simulation can be described
基金Project supported by the National Natural Science Foundation of China.
文摘In this paper we propose a characteristics mixed finite element method to overcome thenumerical dispersion for the 2-phase immiscible displacement. The pressure and associatedfluid velocity will be approximated by a mixed finite element method, and the saturationwill be treated by a backward characteristics method. The L_∞ stability and convergence forthe scheme are proved, and optimal-order error estimates in L_∞ are obtained.
基金supported by the National Natural Science Foundation of China(Grant Nos.51401176,51002128)the Scientific Research Foundation of the Hunan Provincial Education Department(Grant No.17A205)the Natural Science Foundation of Hunan Province(Grant No.2018JJ2393,2018JJ2394)
文摘Although SnO_2-based nanomaterials used to be considered as being extraordinarily versatile for application to nanosensors,microelectronic devices, lithium-ion batteries, supercapacitors and other devices, the functionalities of SnO_2-based nanomaterials are severely limited by their intrinsic vulnerabilities. Facile electrospinning was used to prepare SnO_2 nanofibers coated with a protective carbon layer. The mechanical properties of individual core-shell-structured SnO_2@C nanofibers were investigated by atomic force microscopy and the finite element method. The elastic moduli of the carbon-coated SnO_2 nanofibers remarkably increased, suggesting that coating SnO_2 nanofibers with carbon could be an effective method of improving their mechanical properties.
