In this paper we propose a finite element method for solving elliptic equations with observational Dirichlet boundary data which may subject to random noises.The method is based on the weak formulation of Lagrangian m...In this paper we propose a finite element method for solving elliptic equations with observational Dirichlet boundary data which may subject to random noises.The method is based on the weak formulation of Lagrangian multiplier and requires balanced oversampling of the measurements of the boundary data to control the random noises.We show the convergence of the random finite elemen t error in expec tat ion and,when the noise is subGaussian,in the Orlicz^2-norm which implies the probability that the finite element error estimates are viola ted decays exponentially.Numerical examples are included.展开更多
In this paper we construct optimal, in certain sense, estimates of values of linear functionals on solutions to two-point boundary value problems (BVPs) for systems of linear first-order ordinary differential equation...In this paper we construct optimal, in certain sense, estimates of values of linear functionals on solutions to two-point boundary value problems (BVPs) for systems of linear first-order ordinary differential equations from observations which are linear transformations of the same solutions perturbed by additive random noises. It is assumed here that right-hand sides of equations and boundary data as well as statistical characteristics of random noises in observations are not known and belong to certain given sets in corresponding functional spaces. This leads to the necessity of introducing minimax statement of an estimation problem when optimal estimates are defined as linear, with respect to observations, estimates for which the maximum of mean square error of estimation taken over the above-mentioned sets attains minimal value. Such estimates are called minimax mean square or guaranteed estimates. We establish that the minimax mean square estimates are expressed via solutions of some systems of differential equations of special type and determine estimation errors.展开更多
The objective of this paper is to investigate the turbulent flow structures around the submarine model and evaluate the effect of the yaw angle on the turbulent flow characteristics.The large eddy simulation based on ...The objective of this paper is to investigate the turbulent flow structures around the submarine model and evaluate the effect of the yaw angle on the turbulent flow characteristics.The large eddy simulation based on the boundary data immersion method is used to investigate.The computational domain consists of 1.2×10^(8)uniformly distributed Cartesian orthogonal grid nodes to capture the basic flow characteristics around the model.The pressure coefficient,friction coefficient and wake velocity distribution are in good agreement with the experimental data.Three different types of vortex structures were mainly captured around the model,including horseshoe vortex,sail tip vortex and crossflow separation vortex.With the increase of the yaw angle,the asymmetry of the horseshoe vortex and the tip vortex gradually increases,and the vortex strength of the vortex leg on the windward of the horseshoe vortex and the vortex strength of the tip vortex also increase gradually.For the crossflow separation vortex,the flow separation zone gradually expands and migrates downstream with the increase of the yaw angle.展开更多
基金This work was supported in part by the National Center for Mathematics and Interdisciplinary Sciences,CAS and China NSF under the grant 118311061 and 11501551.
文摘In this paper we propose a finite element method for solving elliptic equations with observational Dirichlet boundary data which may subject to random noises.The method is based on the weak formulation of Lagrangian multiplier and requires balanced oversampling of the measurements of the boundary data to control the random noises.We show the convergence of the random finite elemen t error in expec tat ion and,when the noise is subGaussian,in the Orlicz^2-norm which implies the probability that the finite element error estimates are viola ted decays exponentially.Numerical examples are included.
文摘In this paper we construct optimal, in certain sense, estimates of values of linear functionals on solutions to two-point boundary value problems (BVPs) for systems of linear first-order ordinary differential equations from observations which are linear transformations of the same solutions perturbed by additive random noises. It is assumed here that right-hand sides of equations and boundary data as well as statistical characteristics of random noises in observations are not known and belong to certain given sets in corresponding functional spaces. This leads to the necessity of introducing minimax statement of an estimation problem when optimal estimates are defined as linear, with respect to observations, estimates for which the maximum of mean square error of estimation taken over the above-mentioned sets attains minimal value. Such estimates are called minimax mean square or guaranteed estimates. We establish that the minimax mean square estimates are expressed via solutions of some systems of differential equations of special type and determine estimation errors.
基金supported by the National Key Research and Development Program of China(Grant No.2022YFB3303500)the National Natural Science Foundation of China(Grant No.52279081)the Fundamental Research Funds for the Central Universities(Grant No.2023CX01004).
文摘The objective of this paper is to investigate the turbulent flow structures around the submarine model and evaluate the effect of the yaw angle on the turbulent flow characteristics.The large eddy simulation based on the boundary data immersion method is used to investigate.The computational domain consists of 1.2×10^(8)uniformly distributed Cartesian orthogonal grid nodes to capture the basic flow characteristics around the model.The pressure coefficient,friction coefficient and wake velocity distribution are in good agreement with the experimental data.Three different types of vortex structures were mainly captured around the model,including horseshoe vortex,sail tip vortex and crossflow separation vortex.With the increase of the yaw angle,the asymmetry of the horseshoe vortex and the tip vortex gradually increases,and the vortex strength of the vortex leg on the windward of the horseshoe vortex and the vortex strength of the tip vortex also increase gradually.For the crossflow separation vortex,the flow separation zone gradually expands and migrates downstream with the increase of the yaw angle.
