In this paper, we present the a posteriori error estimate of two-grid mixed finite element methods by averaging techniques for semilinear elliptic equations. We first propose the two-grid algorithms to linearize the m...In this paper, we present the a posteriori error estimate of two-grid mixed finite element methods by averaging techniques for semilinear elliptic equations. We first propose the two-grid algorithms to linearize the mixed method equations. Then, the averaging technique is used to construct the a posteriori error estimates of the two-grid mixed finite element method and theoretical analysis are given for the error estimators. Finally, we give some numerical examples to verify the reliability and efficiency of the a posteriori error estimator.展开更多
In this paper,we investigate a streamline diffusion finite element approxi- mation scheme for the constrained optimal control problem governed by linear con- vection dominated diffusion equations.We prove the existenc...In this paper,we investigate a streamline diffusion finite element approxi- mation scheme for the constrained optimal control problem governed by linear con- vection dominated diffusion equations.We prove the existence and uniqueness of the discretized scheme.Then a priori and a posteriori error estimates are derived for the state,the co-state and the control.Three numerical examples are presented to illustrate our theoretical results.展开更多
A maximum a posteriori（ MAP） algorithm is proposed to improve the accuracy of super resolution（ SR） reconstruction in traditional methods. The algorithm applies both joints image registration and SR reconstruction...A maximum a posteriori（ MAP） algorithm is proposed to improve the accuracy of super resolution（ SR） reconstruction in traditional methods. The algorithm applies both joints image registration and SR reconstruction in the framework,but separates them in the process of iteratiion. Firstly,we estimate the shifting parameters through two lowresolution（ LR） images and use the parameters to reconstruct initial HR images. Then,we update the shifting parameters using HR images. The aforementioned steps are repeated until the ideal HR images are obtained. The metrics such as PSNR and SSIM are used to fully evaluate the quality of the reconstructed image. Experimental results indicate that the proposed method can enhance image resolution efficiently.展开更多
In this paper, a posteriori error estimates for the generalized Schwartz method with Dirichlet boundary conditions on the interfaces for advection-diffusion equation with second order boundary value problems are prove...In this paper, a posteriori error estimates for the generalized Schwartz method with Dirichlet boundary conditions on the interfaces for advection-diffusion equation with second order boundary value problems are proved by using the Euler time scheme combined with Galerkin spatial method. Furthermore, an asymptotic behavior in Sobolev norm is de- duced using Benssoussau-Lions＇ algorithm. Finally, the results of some numerical experiments are presented to support the theory.展开更多
Residual based on a posteriori error estimates for conforming finite element solutions of incompressible Navier-Stokes equations with stream function form which were computed with seven recently proposed two-level met...Residual based on a posteriori error estimates for conforming finite element solutions of incompressible Navier-Stokes equations with stream function form which were computed with seven recently proposed two-level method were derived. The posteriori error estimates contained additional terms in comparison to the error estimates for the solution obtained by the standard finite element method. The importance of these additional terms in the error estimates was investigated by studying their asymptotic behavior. For optimal scaled meshes, these bounds are not of higher order than of convergence of discrete solution.展开更多
A nonlinear Galerkin mixed element (NGME) method and a posteriori error exstimator based on the method are established for the stationary Navier-Stokes equations. The existence and error estimates of the NGME solution...A nonlinear Galerkin mixed element (NGME) method and a posteriori error exstimator based on the method are established for the stationary Navier-Stokes equations. The existence and error estimates of the NGME solution are first discussed, and then a posteriori error estimator based on the NGME method is derived.展开更多
In this paper, a posteriori error estimates were derived for piecewise linear finite element approximations to parabolic obstacle problems. The instrumental ingredient was introduced as a new interpolation operator wh...In this paper, a posteriori error estimates were derived for piecewise linear finite element approximations to parabolic obstacle problems. The instrumental ingredient was introduced as a new interpolation operator which has optimal approximation properties and preserves positivity. With the help of the interpolation operator the upper and lower bounds were obtained.展开更多
A posteriori error estimate of the discontinuous-streamline diffusion method for first-order hyperbolic equations was presented, which can be used to adjust space mesh reasonably. A numerical example is given to illus...A posteriori error estimate of the discontinuous-streamline diffusion method for first-order hyperbolic equations was presented, which can be used to adjust space mesh reasonably. A numerical example is given to illustrate the accuracy and feasibility of this method.展开更多
In this article, we use streamline diffusion method for the linear second order hyperbolic initial-boundary value problem. More specifically, we prove a posteriori error estimates for this method for the linear wave e...In this article, we use streamline diffusion method for the linear second order hyperbolic initial-boundary value problem. More specifically, we prove a posteriori error estimates for this method for the linear wave equation. We observe that this error estimates make finite element method increasingly powerful rather than other methods.展开更多
The main aim of this paper is to give an anisotropic posteriori error estimator. We firstly study the convergence of bilineax finite element for the second order problem under anisotropic meshes. By using some novel a...The main aim of this paper is to give an anisotropic posteriori error estimator. We firstly study the convergence of bilineax finite element for the second order problem under anisotropic meshes. By using some novel approaches and techniques, the optimal error estimates and some superconvergence results axe obtained without the regulaxity assumption and quasi-uniform assumption requirements on the meshes. Then, based on these results, we give an anisotropic posteriori error estimate for the second problem.展开更多
Interferogram noise reduction is a very important processing step in Interferometric Synthetic Aperture Radar(InSAR) technique. The most difficulty for this step is to remove the noises and preserve the fringes simult...Interferogram noise reduction is a very important processing step in Interferometric Synthetic Aperture Radar(InSAR) technique. The most difficulty for this step is to remove the noises and preserve the fringes simultaneously. To solve the dilemma, a new interferogram noise reduction algorithm based on the Maximum A Posteriori(MAP) estimate is introduced in this paper. The algorithm is solved under the Total Generalized Variation(TGV) minimization assumption, which exploits the phase characteristics up to the second order differentiation. The ideal noise-free phase consisting of piecewise smooth areas is involved in this assumption, which is coincident with the natural terrain. In order to overcome the phase wraparound effect, complex plane filter is utilized in this algorithm. The simulation and real data experiments show the algorithm can reduce the noises effectively and meanwhile preserve the interferogram fringes very well.展开更多
The paper presents an algorithm of automatic target detection in Synthetic Aperture Radar(SAR) images based on Maximum A Posteriori(MAP). The algorithm is divided into three steps. First, it employs Gaussian mixture d...The paper presents an algorithm of automatic target detection in Synthetic Aperture Radar(SAR) images based on Maximum A Posteriori(MAP). The algorithm is divided into three steps. First, it employs Gaussian mixture distribution to approximate and estimate multi-modal histogram of SAR image. Then, based on the principle of MAP, when a priori probability is both unknown and learned respectively, the sample pixels are classified into different classes c = {target,shadow, background}. Last, it compares the results of two different target detections. Simulation results preferably indicate that the presented algorithm is fast and robust, with the learned a priori probability, an approach to target detection is reliable and promising.展开更多
文摘In this paper, we present the a posteriori error estimate of two-grid mixed finite element methods by averaging techniques for semilinear elliptic equations. We first propose the two-grid algorithms to linearize the mixed method equations. Then, the averaging technique is used to construct the a posteriori error estimates of the two-grid mixed finite element method and theoretical analysis are given for the error estimators. Finally, we give some numerical examples to verify the reliability and efficiency of the a posteriori error estimator.
基金supported by the National Natural Science Foundation of the People’s Republic of China“The research of finite element methods for eigenvalue problems in inverse scattering”(12261024)。
基金supported by the National Basic Research Program under the Grant 2005CB321701the National Natural Science Foundation of China under the Grants 60474027 and 10771211.
文摘In this paper,we investigate a streamline diffusion finite element approxi- mation scheme for the constrained optimal control problem governed by linear con- vection dominated diffusion equations.We prove the existence and uniqueness of the discretized scheme.Then a priori and a posteriori error estimates are derived for the state,the co-state and the control.Three numerical examples are presented to illustrate our theoretical results.
基金Supported by the National Natural Science Foundation of China(61405191)
文摘A maximum a posteriori（ MAP） algorithm is proposed to improve the accuracy of super resolution（ SR） reconstruction in traditional methods. The algorithm applies both joints image registration and SR reconstruction in the framework,but separates them in the process of iteratiion. Firstly,we estimate the shifting parameters through two lowresolution（ LR） images and use the parameters to reconstruct initial HR images. Then,we update the shifting parameters using HR images. The aforementioned steps are repeated until the ideal HR images are obtained. The metrics such as PSNR and SSIM are used to fully evaluate the quality of the reconstructed image. Experimental results indicate that the proposed method can enhance image resolution efficiently.
文摘In this paper, a posteriori error estimates for the generalized Schwartz method with Dirichlet boundary conditions on the interfaces for advection-diffusion equation with second order boundary value problems are proved by using the Euler time scheme combined with Galerkin spatial method. Furthermore, an asymptotic behavior in Sobolev norm is de- duced using Benssoussau-Lions＇ algorithm. Finally, the results of some numerical experiments are presented to support the theory.
文摘Residual based on a posteriori error estimates for conforming finite element solutions of incompressible Navier-Stokes equations with stream function form which were computed with seven recently proposed two-level method were derived. The posteriori error estimates contained additional terms in comparison to the error estimates for the solution obtained by the standard finite element method. The importance of these additional terms in the error estimates was investigated by studying their asymptotic behavior. For optimal scaled meshes, these bounds are not of higher order than of convergence of discrete solution.
文摘A nonlinear Galerkin mixed element (NGME) method and a posteriori error exstimator based on the method are established for the stationary Navier-Stokes equations. The existence and error estimates of the NGME solution are first discussed, and then a posteriori error estimator based on the NGME method is derived.
基金Project supported by National Natural Science Foundation ofChina (Grant No .10471089)
文摘In this paper, a posteriori error estimates were derived for piecewise linear finite element approximations to parabolic obstacle problems. The instrumental ingredient was introduced as a new interpolation operator which has optimal approximation properties and preserves positivity. With the help of the interpolation operator the upper and lower bounds were obtained.
文摘A posteriori error estimate of the discontinuous-streamline diffusion method for first-order hyperbolic equations was presented, which can be used to adjust space mesh reasonably. A numerical example is given to illustrate the accuracy and feasibility of this method.
文摘In this article, we use streamline diffusion method for the linear second order hyperbolic initial-boundary value problem. More specifically, we prove a posteriori error estimates for this method for the linear wave equation. We observe that this error estimates make finite element method increasingly powerful rather than other methods.
文摘The main aim of this paper is to give an anisotropic posteriori error estimator. We firstly study the convergence of bilineax finite element for the second order problem under anisotropic meshes. By using some novel approaches and techniques, the optimal error estimates and some superconvergence results axe obtained without the regulaxity assumption and quasi-uniform assumption requirements on the meshes. Then, based on these results, we give an anisotropic posteriori error estimate for the second problem.
文摘Interferogram noise reduction is a very important processing step in Interferometric Synthetic Aperture Radar(InSAR) technique. The most difficulty for this step is to remove the noises and preserve the fringes simultaneously. To solve the dilemma, a new interferogram noise reduction algorithm based on the Maximum A Posteriori(MAP) estimate is introduced in this paper. The algorithm is solved under the Total Generalized Variation(TGV) minimization assumption, which exploits the phase characteristics up to the second order differentiation. The ideal noise-free phase consisting of piecewise smooth areas is involved in this assumption, which is coincident with the natural terrain. In order to overcome the phase wraparound effect, complex plane filter is utilized in this algorithm. The simulation and real data experiments show the algorithm can reduce the noises effectively and meanwhile preserve the interferogram fringes very well.
文摘The paper presents an algorithm of automatic target detection in Synthetic Aperture Radar(SAR) images based on Maximum A Posteriori(MAP). The algorithm is divided into three steps. First, it employs Gaussian mixture distribution to approximate and estimate multi-modal histogram of SAR image. Then, based on the principle of MAP, when a priori probability is both unknown and learned respectively, the sample pixels are classified into different classes c = {target,shadow, background}. Last, it compares the results of two different target detections. Simulation results preferably indicate that the presented algorithm is fast and robust, with the learned a priori probability, an approach to target detection is reliable and promising.
