检索结果-南通市图书馆

NONCONFORMING FINITE ELEMENT PENALTY METHOD FOR stokes equation

在线全文

学校读者我要写书评

暂无评论

Applied Mathematics(A Journal of Chinese Universities) 1998年第1期13卷 53-58页

作者： SHI DONGYANG, FENG WEIBING AND LI KAITAI Department of Applied Mathematics Xi’an Jiaotong University Xi’an

a special penalty method is presented to improve the accuracy of the standard penalty method for solving stokes equation with nonconforming finite *** is shown that this method with a larger penalty parameter can achieve the same accuracy as the standard method with a smaller penalty parameter. The convergence rate of the standard method is just half order of this penalty method when using the same penalty parameter, while the extrapolation method proposed by Faik et al can not yield so high accuracy of *** last, we also get the super convergence estimates for total flux. Received October 14, 1996 1991 MR Subject Classification: 65N30.

关键词： Special method stokes equation standard method.

FINITE VOLUME METHOD BASED ON THE CROUZEIX-RAVIART ELEMENT FOR THE stokes equation

在线全文

学校读者我要写书评

暂无评论

Journal of Zhejiang University-Science A(Applied Physics & Engineering) 2001年第2期2卷 45-49页

作者：李大明 Dept. of Mathmatics Zhejiang University Hangzhou China

The author provides a new discretization method-the finite volume method(FVM).For the stokes equation the velocity space is approximated by the nonconforming linear element based on the dual partition and the pressure by the piecewise constant based on the primal triangulation .Under the suitable smoothness of the solution, the optimal convergence rate \%O(h)\% is obtained,where \%h\% denotes the parameter of the space discretization.

关键词： stokes equation finite volume method Crouzeix-Raviart element

Application of Splitting Extrapolation to stokes equation

在线全文

同方期刊数据库

学校读者我要写书评

暂无评论

Wuhan University Journal of Natural Sciences 2003年第1A期8卷 1-4页

作者： Chen Jian\|ye, Xu Di\|hong, Sun Le\|lin School of Mathematics and Statistics, Wuhan University, Whuhan 430072, Hubei, China School of Mathematics and Statistics Wuhan University Whuhan 430072 Hubei China

This paper deals with the splitting extrapolation for mixed finite element used in the approximation of the steady stokes equation. Applying the multi variate asymptotic expansion of the error on independent grid p... 详细信息

关键词： splitting extrapolation domain decomposition mixed finite element stokes equation

Convergence Analysis and Error Estimate for Distributed Optimal Control Problems Governed by stokes equations with Velocity-Constraint

在线全文

学校读者我要写书评

暂无评论

Advances in Applied Mathematics and Mechanics 2022年第1期14卷 33-55页

作者： Liang Ge Haifeng Niu Jianwei Zhou School of Mathematical Sciences University of JinanJinan 250022ShandongChina School of Mathematics and Information Science Henan Polytechnic UniversityJiaozuo 454000HenanChina School of Mathematics and Statistics Linyi UniversityLinyi 276005ShandongChina Division of Applied and Computational Mathematics Beijing Computational Science Research CenterBeijing 100193China

In this paper,spectral approximations for distributed optimal control problems governed by the stokes equation are *** the constraint set on velocity is stated with *** conditions of the continuous and discretized systems are deduced with the Karush-Kuhn-Tucker conditions and a Lagrange multiplier depending on the *** solve the equivalent systems with high accuracy,Galerkin spectral approximations are employed to discretize the constrained optimal control ***,we adopt a parameter l in the pressure approximation space,which also guarantees the inf-sup condition,and study a priori error estimates for the velocity and ***,an efficient algorithm based on the Uzawa algorithm is proposed and its convergence results are investigated with rigorous *** experiments are performed to confirm the theoretical results.

关键词： Optimal control spectral approximation stokes equation convergence analysis

REMARK ON UNIQUE CONTINUATION OF SOLUTIONS TO THE stokes AND THE NAVIER-stokes equationS

在线全文

维普期刊数据库

学校读者我要写书评

暂无评论

Acta Mathematica Scientia 2005年第4期25卷 594-598页

作者： Jin Kim Tu 常谦顺 TuInstitute of Mathematics Academy of Sciences of DPR of Korea Pyonyang DPR of Korea Institute of Applied Mathematics Academy of Mathematics and System SciencesChinese Academy of Sciences Beijing 100080 China

New simple proofs of unique continuation of solutions for the stokes equation and Navier-stokes equations is presented under weaker conditions.

关键词： stokes equation Navier-stokes equation

ON DISTRIBUTED H^(1) SHAPE GRADIENT FLOWS IN OPTIMAL SHAPE DESIGN OF stokes FLOWS:CONVERGENCE ANALYSIS AND NUMERICAL APPLICATIONS

在线全文

学校读者我要写书评

暂无评论

Journal of Computational Mathematics 2022年第2期40卷 231-257页

作者： Jiajie Li Shengfeng Zhu School of Mathematical Sciences East China Normal UniversityShanghai 200241China

We consider optimal shape design in stokes flow using H^(1) shape gradient flows based on the distributed Eulerian *** element is used for discretizations of stokes equation and Galerkin finite element is used for discretizations of distributed and boundary H^(1) shape gradient *** analysis with a priori error estimates is provided under general and different regularity *** investigate the performances of shape gradient descent algorithms for energy dissipation minimization and obstacle *** comparisons in 2D and 3D show that the distributed H1 shape gradient flow is more accurate than the popular boundary *** corresponding distributed shape gradient algorithm is more effective.

关键词： Shape optimization stokes equation Distributed shape gradient Finite element MINI element Eulerian derivative

Investigating and Mitigating Failure Modes in Physics-Informed Neural Networks(PINNs)

在线全文

维普期刊数据库

学校读者我要写书评

暂无评论

Communications in Computational Physics 2023年第5期33卷 1240-1269页

作者： Shamsulhaq Basir Mechanical Engineering and Materials Science Department at the University of Pittsburgh PittsburghPA 15261USA

This paper explores the difficulties in solving partial differential equations(PDEs)using physics-informed neural networks(PINNs).PINNs use physics as a regularization term in the objective ***,a drawback of this approach is the requirement for manual hyperparameter tuning,making it impractical in the absence of validation data or prior knowledge of the *** investigations of the loss landscapes and backpropagated gradients in the presence of physics reveal that existing methods produce non-convex loss landscapes that are hard to *** findings demonstrate that high-order PDEs contaminate backpropagated gradients and hinder *** address these challenges,we introduce a novel method that bypasses the calculation of high-order derivative operators and mitigates the contamination of backpropagated ***,we reduce the dimension of the search space and make learning PDEs with non-smooth solutions *** method also provides a mechanism to focus on complex regions of the ***,we present a dual unconstrained formulation based on Lagrange multiplier method to enforce equality constraints on the model’s prediction,with adaptive and independent learning rates inspired by adaptive subgradient *** apply our approach to solve various linear and non-linear PDEs.

关键词： Constrained optimization Lagrangian multiplier method stokes equation convection equation convection-dominated convection-diffusion equation heat transfer in composite medium Lid-driven cavity problem

Approximate Analytical Solutions to the Heat and stokes equations on the Half-Line Obtained by Fokas’ Transform

在线全文

维普期刊数据库

学校读者我要写书评

暂无评论

Journal of Applied Mathematics and Physics 2021年第4期9卷 809-833页

作者： Mohamed Lachaab Marius Beceanu University of Tunis Tunis Tunisia University at Albany New York USA

In this paper, we evaluate the integrals that are solutions of the heat and stokes’ equations obtained by Fokas’ transform method by deriving exact formulas. Our method is more accurate and efficient than the contour deformation and parametrization used by Fokas to compute these integrals. In fact, for the heat equation, our solution is exact up to the imaginary error function and for the stokes equation, our solution is exact up to the incomplete Airy function. In addition, our solutions extend to the lateral boundary without convergence issues, allow for asymptotic expansions, and are much faster than those obtained by other methods.

关键词： Heat equation stokes equation Fokas’ Transform Asymptotic Expansion Hilbert Transform Incomplete Airy Function Imaginary Error Function

NON-STATIONARY stokes FLOWS UNDER LEAK BOUNDARY CONDITIONS OF FRICTION TYPE

在线全文

维普期刊数据库

学校读者我要写书评

暂无评论

Journal of Computational Mathematics 2001年第1期19卷 1-8页

作者： Hiroshi Fujita (The Research institute of Educational Development, Tokai University, Shibuya-ku, Tokyo 151-0063, Japan) Tokai University 日本 151-0063

Examines the initial value problem for non-stationary stokes flows, under a non-linear boundary conditions which can be called the leak boundary condition of friction type. Examination of the solvability of the initia... 详细信息

关键词： stokes equation leak boundary condition nonlinear semigroup