In this paper, we consider the Cauchy problem for the Laplace equation, which is severely ill-posed in the sense that the solution does not depend continuously on the data. A modified Tikhonov regularization method is...In this paper, we consider the Cauchy problem for the Laplace equation, which is severely ill-posed in the sense that the solution does not depend continuously on the data. A modified Tikhonov regularization method is proposed to solve this problem. An error estimate for the a priori parameter choice between the exact solution and its regularized approximation is obtained. Moreover, an a posteriori parameter choice rule is proposed and a stable error estimate is also obtained. Numerical examples illustrate the validity and effectiveness of this method.展开更多
A least-squares mixed finite element (LSMFE) method for the numerical solution of fourth order parabolic problems analyzed and developed in this paper. The Ciarlet-Raviart mixed finite element space is used to approxi...A least-squares mixed finite element (LSMFE) method for the numerical solution of fourth order parabolic problems analyzed and developed in this paper. The Ciarlet-Raviart mixed finite element space is used to approximate. The a posteriori error estimator which is needed in the adaptive refinement algorithm is proposed. The local evaluation of the least-squares functional serves as a posteriori error estimator. The posteriori errors are effectively estimated. The convergence of the adaptive least-squares mixed finite element method is proved.展开更多
Peak to Average Power Ratio (PAPR) is defined as the instantaneous power (maximum value) to the average power ratio. PAPR is considered to be a major problem in OFDM systems. This problem can cause radical unexpected ...Peak to Average Power Ratio (PAPR) is defined as the instantaneous power (maximum value) to the average power ratio. PAPR is considered to be a major problem in OFDM systems. This problem can cause radical unexpected behavior of the signal fluctuation. This fluctuation is constituted by a large number of power states. The enormous number of these states leads to an additional complexity of ADCs and DACs. This research addresses the previous problem in OFDM systems utilizing Turbo Codes. μLaCP technique is employed for the purpose of decreasing PAPR. Moreover, our OFDM system was simulated in the presence of an AWGN channel with four types of codes (without the presence of ADCs and DACs). These were constituted of PCCC (typical and new), SCCC, and Convolutional Codes. Our Turbo Coded OFDM exhibited unchanged BER performance before and after the use of μLaCP technique. This was accomplished by modifying our previous PAPR reduction technique without sacrificing greatly its attributes.展开更多
In this paper, we investigate a priori error estimates and superconvergence properties for a model optimal control problem of bilinear type, which includes some parameter estimation application. The state and co-state...In this paper, we investigate a priori error estimates and superconvergence properties for a model optimal control problem of bilinear type, which includes some parameter estimation application. The state and co-state are discretized by piecewise linear functions and control is approximated by piecewise constant functions. We derive a priori error estimates and superconvergence analysis for both the control and the state approximations. We also give the optimal L^2-norm error estimates and the almost optimal L^∞-norm estimates about the state and co-state. The results can be readily used for constructing a posteriori error estimators in adaptive finite element approximation of such optimal control problems.展开更多
Four primal discontinuous Galerkin methods are applied to solve reactive transport problems, namely, Oden-BabuSka-Baumann DG （OBB-DG）, non-symmetric interior penalty Galerkin （NIPG）, symmetric interior penalty Gal...Four primal discontinuous Galerkin methods are applied to solve reactive transport problems, namely, Oden-BabuSka-Baumann DG （OBB-DG）, non-symmetric interior penalty Galerkin （NIPG）, symmetric interior penalty Galerkin （SIPG）, and incomplete interior penalty Galerkin （IIPG）. A unified a posteriori residual-type error estimation is derived explicitly for these methods. From the computed solution and given data, explicit estimators can be computed efficiently and directly, which can be used as error indicators for adaptation. Unlike in the reference [10], we obtain the error estimators in L^2 （L^2） norm by using duality techniques instead of in L^2（H^1） norm.展开更多
This paper presents a posteriori error estimate of FD-SD method for two-dimensional time-dependent convection-dominated diffusion equation, which can be used to reasonably adjust space mesh. The numerical result shows...This paper presents a posteriori error estimate of FD-SD method for two-dimensional time-dependent convection-dominated diffusion equation, which can be used to reasonably adjust space mesh. The numerical result shows that this local refinement is accurate and feasible.展开更多
We consider an Adaptive Edge Finite Element Method （AEFEM） for the 3D eddy currents equations with variable coefficients using a residual-type a posteriori error estimator. Both the components of the estimator and c...We consider an Adaptive Edge Finite Element Method （AEFEM） for the 3D eddy currents equations with variable coefficients using a residual-type a posteriori error estimator. Both the components of the estimator and certain oscillation terms, due to the occurrence of the variable coefficients, have to be controlled properly within the adaptive loop which is taken care of by appropriate bulk criteria. Convergence of the AEFEM in terms of reductions of the energy norm of the discretization error and of the oscillations is shown. Numerical results are given to illustrate the performance of the AEFEM.展开更多
In this paper, we study adaptive finite element discretization schemes for an optimal control problem governed by elliptic PDE with an integral constraint for the state. We derive the equivalent a posteriori error est...In this paper, we study adaptive finite element discretization schemes for an optimal control problem governed by elliptic PDE with an integral constraint for the state. We derive the equivalent a posteriori error estimator for the finite element approximation, which particularly suits adaptive multi-meshes to capture different singularities of the control and the state. Numerical examples are presented to demonstrate the efficiency of a posteriori error estimator and to confirm the theoretical results.展开更多
The paper presents a posteriori error estimate of FD-SD method for one- dimension time-dependent convection- dominated diffusion equation 5 which can be used to adjust space mesh. Some numerical results and an algorit...The paper presents a posteriori error estimate of FD-SD method for one- dimension time-dependent convection- dominated diffusion equation 5 which can be used to adjust space mesh. Some numerical results and an algorithm of adaptive finite element method based on this a posteriori error estimate are given.展开更多
基金supported by the National Natural Science Foundation of China(1117113611261032)+2 种基金the Distinguished Young Scholars Fund of Lan Zhou University of Technology(Q201015)the basic scientific research business expenses of Gansu province collegethe Natural Science Foundation of Gansu province(1310RJYA021)
文摘In this paper, we consider the Cauchy problem for the Laplace equation, which is severely ill-posed in the sense that the solution does not depend continuously on the data. A modified Tikhonov regularization method is proposed to solve this problem. An error estimate for the a priori parameter choice between the exact solution and its regularized approximation is obtained. Moreover, an a posteriori parameter choice rule is proposed and a stable error estimate is also obtained. Numerical examples illustrate the validity and effectiveness of this method.
文摘A least-squares mixed finite element (LSMFE) method for the numerical solution of fourth order parabolic problems analyzed and developed in this paper. The Ciarlet-Raviart mixed finite element space is used to approximate. The a posteriori error estimator which is needed in the adaptive refinement algorithm is proposed. The local evaluation of the least-squares functional serves as a posteriori error estimator. The posteriori errors are effectively estimated. The convergence of the adaptive least-squares mixed finite element method is proved.
文摘Peak to Average Power Ratio (PAPR) is defined as the instantaneous power (maximum value) to the average power ratio. PAPR is considered to be a major problem in OFDM systems. This problem can cause radical unexpected behavior of the signal fluctuation. This fluctuation is constituted by a large number of power states. The enormous number of these states leads to an additional complexity of ADCs and DACs. This research addresses the previous problem in OFDM systems utilizing Turbo Codes. μLaCP technique is employed for the purpose of decreasing PAPR. Moreover, our OFDM system was simulated in the presence of an AWGN channel with four types of codes (without the presence of ADCs and DACs). These were constituted of PCCC (typical and new), SCCC, and Convolutional Codes. Our Turbo Coded OFDM exhibited unchanged BER performance before and after the use of μLaCP technique. This was accomplished by modifying our previous PAPR reduction technique without sacrificing greatly its attributes.
基金the National Basic Research Program under the Grant 2005CB321703the NSFC under the Grants 10571108 and 10441005the Research Fund for Doctoral Program of High Education by China State Education Ministry under the Grant 2005042203
文摘In this paper, we investigate a priori error estimates and superconvergence properties for a model optimal control problem of bilinear type, which includes some parameter estimation application. The state and co-state are discretized by piecewise linear functions and control is approximated by piecewise constant functions. We derive a priori error estimates and superconvergence analysis for both the control and the state approximations. We also give the optimal L^2-norm error estimates and the almost optimal L^∞-norm estimates about the state and co-state. The results can be readily used for constructing a posteriori error estimators in adaptive finite element approximation of such optimal control problems.
基金This work is supported by Program for New Century Excellent Talents in University of China State Education Ministry NCET-04-0776, National Science Foundation of China, the National Basic Research Program under the Grant 2005CB321703, and the key project of China State Education Ministry and Hunan Education Commission.
文摘Four primal discontinuous Galerkin methods are applied to solve reactive transport problems, namely, Oden-BabuSka-Baumann DG （OBB-DG）, non-symmetric interior penalty Galerkin （NIPG）, symmetric interior penalty Galerkin （SIPG）, and incomplete interior penalty Galerkin （IIPG）. A unified a posteriori residual-type error estimation is derived explicitly for these methods. From the computed solution and given data, explicit estimators can be computed efficiently and directly, which can be used as error indicators for adaptation. Unlike in the reference [10], we obtain the error estimators in L^2 （L^2） norm by using duality techniques instead of in L^2（H^1） norm.
文摘This paper presents a posteriori error estimate of FD-SD method for two-dimensional time-dependent convection-dominated diffusion equation, which can be used to reasonably adjust space mesh. The numerical result shows that this local refinement is accurate and feasible.
基金The work of the first author was supported by the NSF under Grant No.DMS-0411403 and Grant No.DMS-0511611The second author acknowledges the support from the Austrian Science Foundation(FWF)under Grant No.Start Y-192Both authors acknowledge support and the inspiring athmosphere at the Johann Radon Institute for Computational and Applied Mathematics(RICAM),Linz,Austria,during the special semester on computational mechanics
文摘We consider an Adaptive Edge Finite Element Method （AEFEM） for the 3D eddy currents equations with variable coefficients using a residual-type a posteriori error estimator. Both the components of the estimator and certain oscillation terms, due to the occurrence of the variable coefficients, have to be controlled properly within the adaptive loop which is taken care of by appropriate bulk criteria. Convergence of the AEFEM in terms of reductions of the energy norm of the discretization error and of the oscillations is shown. Numerical results are given to illustrate the performance of the AEFEM.
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 of P.R.China under the grant 2005CB321703the NSFC under the grants:10441005 and 10571108the Research Fund for Doctoral Program of High Education by China State Education Ministry
文摘In this paper, we study adaptive finite element discretization schemes for an optimal control problem governed by elliptic PDE with an integral constraint for the state. We derive the equivalent a posteriori error estimator for the finite element approximation, which particularly suits adaptive multi-meshes to capture different singularities of the control and the state. Numerical examples are presented to demonstrate the efficiency of a posteriori error estimator and to confirm the theoretical results.
文摘The paper presents a posteriori error estimate of FD-SD method for one- dimension time-dependent convection- dominated diffusion equation 5 which can be used to adjust space mesh. Some numerical results and an algorithm of adaptive finite element method based on this a posteriori error estimate are given.
