Article
Mathematics, Applied
Akram Boukabache
Summary: This paper introduces and analyzes a novel discrete formulation for stabilizing the collocated finite volume method for the stationary Stokes problem. The method is based on the lowest equal-order approximation for both velocity and pressure unknowns, and introduces a macro-volume condition to build the local stabilized finite volume formulation. The paper proves the stability of the scheme, the existence and uniqueness of the discrete solution, and derives the error estimate of the formulation.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2022)
Article
Mathematics, Applied
Rodolfo Araya, Cristian Carcamo, Abner H. Poza
Summary: In this work, a new stabilized finite element scheme is introduced and analyzed for the Stokes-Temperature coupled problem. The scheme allows for equal-order interpolation to approximate the velocity, pressure, temperature, and stress. An equivalent variational formulation of the coupled problem is analyzed, inspired by ideas proposed in [3]. Existence of the discrete solution is proved, decoupling the proposed stabilized scheme and utilizing continuous dependence results and Brouwer's theorem. Optimal convergence is also proved under classic regularity assumptions of the solution. Numerical examples are presented to demonstrate the quality of the scheme, including a comparison to a standard reference in geosciences described in [38].
APPLIED NUMERICAL MATHEMATICS
(2023)
Article
Mathematics, Applied
Liming Guo, Wenbin Chen
Summary: In this paper, a decoupled stabilized finite element method is proposed for solving the time-dependent Navier-Stokes/Biot problem. The coupling problem is divided into two subproblems and solved using different numerical methods. The stability analysis and error estimates are provided to validate the effectiveness of the proposed method.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2022)
Article
Mathematics, Applied
Alejandro Allendes, Gabriel R. Barrenechea, Julia Novo
Summary: This work focuses on the finite element discretization of the incompressible Navier-Stokes equations, using a low order stabilized finite element method with piecewise linear continuous discrete velocities and piecewise constant pressures. The modified continuity equation involves a stabilizing bilinear form based on the jumps of the pressure, resulting in a divergence-free velocity field. The stability of the discrete problem is proven without needing to rewrite the convective field in its skew-symmetric way, and error estimates with constants independent of viscosity are established and validated through numerous numerical experiments.
SIAM JOURNAL ON SCIENTIFIC COMPUTING
(2021)
Article
Mathematics, Applied
Hongtao Yang, Yonghai Li
Summary: In this paper, the MINI mixed finite volume element methods (MINI-FVEM) for Stokes problem on triangular meshes are introduced and analyzed. The trial spaces for velocity and pressure are chosen as the MINI element pair, and the test spaces for velocity and pressure are taken as the piecewise constant function spaces on the respective dual grid. Equivalence of bilinear forms and inf-sup conditions are established using new transformation operators. Stability and convergence analysis are conducted based on element analysis methods. Numerical experiments are conducted to illustrate the theoretical results.
INTERNATIONAL JOURNAL OF NUMERICAL ANALYSIS AND MODELING
(2023)
Article
Mathematics, Applied
Michael Neilan, M. Baris Otus
Summary: This paper extends the isoparametric framework to construct a stable, H-1-conforming, and divergence-free method for the Stokes problem in two dimensions based on the Scott-Vogelius pair on Clough-Tocher splits. The pressure space is defined through composition, whereas the velocity space is constructed via a new divergence-preserving mapping that imposes full continuity across shared edges in the isoparametric mesh. Our construction is motivated by operators and spaces found in isoparametric C-1 finite element methods. We prove the method is stable, pressure-robust, and has optimal order convergence. Numerical experiments are provided which confirm the theoretical results.
Article
Physics, Multidisciplinary
Guoliang He, Yong Zhang
Summary: This paper proves the optimal estimations of a low-order spatial-temporal fully discrete method for the non-stationary Navier-Stokes Problem. The semi-implicit scheme based on Euler method is adopted for time discretization, while the special finite volume scheme is adopted for space discretization. The theoretical analysis results show that under certain conditions, the full discretization proposed here has the characteristics of local stability, and the optimal theoretical and numerical error estimation of velocity and pressure can be obtained.
Article
Mathematics, Applied
Xiaofeng Jia, Hui Feng
Summary: This paper presents and analyzes a stabilized SCNLF method for the non-stationary Navier-Stokes/Darcy model. The coupling model is decomposed into Navier-Stokes and Darcy equations, and a second-order partitioned method is obtained through spatial discretization by stabilized finite element method and temporal discretization by CNLF method. The stability and error estimate of the numerical method are provided, and numerical tests are conducted to verify the theoretical analysis.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2022)
Article
Mathematics, Applied
Shahid Hussain, Md Abdullah Al Mahbub, Feng Shi
Summary: In this article, a stabilized finite element method is presented to solve the Stokes-Stokes interface system. By introducing a stabilization term and a consistency term, the instability of the system is addressed, ensuring the well-posedness of the algorithm. The proposed stabilized scheme is shown to have continuity and weak coercivity, and optimal convergence analysis is performed.
JOURNAL OF MATHEMATICAL FLUID MECHANICS
(2022)
Article
Mathematics, Applied
Min Ling, Weimin Han, Shengda Zeng
Summary: This paper presents a pressure projection stabilized mixed finite element method for solving a hemivariational inequality of the stationary Stokes equations with a nonlinear non-monotone slip boundary condition. The paper provides an existence result and a unique solvability analysis for the numerical method, and derives an optimal order error estimate for the numerical solution. Numerical results confirm the theoretical prediction of the convergence order.
JOURNAL OF SCIENTIFIC COMPUTING
(2022)
Article
Mathematics, Applied
Hui Peng, Qilong Zhai, Ran Zhang, Shangyou Zhang
Summary: This paper proposes a new numerical scheme for the coupled Stokes-Darcy model with the Beavers-Joseph-Saffman interface condition, and validates the theoretical analysis through numerical experiments.
SCIENCE CHINA-MATHEMATICS
(2021)
Article
Mathematics
Juan Wen, Pengzhan Huang, Ya-Ling He
Summary: This paper introduces a new stabilized finite element method for the Stokes eigenvalue problem, which is based on multiscale enrichment. The method is also combined with a two-level method to create a new two-level stabilized finite element method for the problem. The theoretical analysis and numerical examples demonstrate the high effectiveness of these new methods.
ACTA MATHEMATICA SCIENTIA
(2021)
Article
Mathematics, Applied
Xiaoxiao He, Fei Song, Weibing Deng
Summary: In this paper, a stabilized extended finite element method is proposed for Stokes interface problems on unfitted triangulation elements. The method does not require the interface to align with the triangulation, and additional stabilization terms are added in the discrete bilinear form. The results show inf-sup stability, optimal error estimates, and uniform errors in energy norm for velocity and in L-2 norm for pressure with respect to viscosity and interface location.
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B
(2022)
Article
Chemistry, Physical
Jungki Lee, Mingu Han
Summary: This paper introduces the use of the volume integral equation method for numerical analysis of isotropic solids with various spheroidal inclusions. The results obtained using VIEM can be used as reference values for verifying similar research.
Article
Mathematics, Applied
Thirupathi Gudi, Ramesh Ch. Sau
Summary: In this paper, a finite element analysis is presented for a Dirichlet boundary control problem governed by the Stokes equation. The control is considered in a convex closed subset of the energy space H-1(Omega). The authors introduce the Stokes problem with outflow condition and control on the Dirichlet boundary to overcome the limited regularity of previous control formulations. The theoretical results are validated by numerical tests.
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2023)
Article
Automation & Control Systems
Lixin Tang, Xianpeng Wang, Zhiming Dong
IEEE TRANSACTIONS ON CYBERNETICS
(2019)
Article
Management
Defeng Sun, Lixin Tang, Roberto Baldacci
EUROPEAN JOURNAL OF OPERATIONAL RESEARCH
(2019)
Article
Automation & Control Systems
Chang Liu, Lixin Tang, Jiyin Liu, Zhenhao Tang
IEEE TRANSACTIONS ON AUTOMATION SCIENCE AND ENGINEERING
(2019)
Article
Metallurgy & Metallurgical Engineering
Yan-he Jia, Li-xin Tang, Zhe George Zhang, Xiao-feng Chen
JOURNAL OF IRON AND STEEL RESEARCH INTERNATIONAL
(2019)
Article
Computer Science, Artificial Intelligence
Qiong Xia, Xianpeng Wang, Lixin Tang
Article
Engineering, Chemical
Shengnan Zhao, M. Paz Ochoa, Lixin Tang, Irene Lotero, Ajit Gopalakrishnan, Ignacio E. Grossmann
INDUSTRIAL & ENGINEERING CHEMISTRY RESEARCH
(2019)
Article
Engineering, Industrial
Peixin Ge, Ying Meng, Jiyin Liu, Lixin Tang, Ren Zhao
INTERNATIONAL JOURNAL OF PRODUCTION RESEARCH
(2020)
Article
Engineering, Industrial
Yanyan Zhang, Gary G. Yen, Lixin Tang
INTERNATIONAL JOURNAL OF PRODUCTION RESEARCH
(2020)
Article
Engineering, Multidisciplinary
L. J. Tang, X. P. Wang, L. X. Tang, C. Cheng, Y. Yang
ENGINEERING OPTIMIZATION
(2020)
Article
Computer Science, Information Systems
Fei Zou, Gary G. Yen, Lixin Tang
INFORMATION SCIENCES
(2020)
Article
Economics
Defeng Sun, Ying Meng, Lixin Tang, Jinyin Liu, Baobin Huang, Jiefu Yang
TRANSPORTATION RESEARCH PART E-LOGISTICS AND TRANSPORTATION REVIEW
(2020)
Article
Automation & Control Systems
Chang Liu, Lixin Tang, Jiyin Liu
IEEE TRANSACTIONS ON AUTOMATION SCIENCE AND ENGINEERING
(2020)
Article
Automation & Control Systems
Guodong Zhao, Jiyin Liu, Lixin Tang, Ren Zhao, Yun Dong
IEEE TRANSACTIONS ON AUTOMATION SCIENCE AND ENGINEERING
(2020)
Proceedings Paper
Computer Science, Information Systems
Zuocheng Li, Lixin Tang
2019 IEEE INTERNATIONAL CONFERENCE ON INDUSTRIAL CYBER PHYSICAL SYSTEMS (ICPS 2019)
(2019)
Article
Computer Science, Information Systems
Linlin Li, Zan Wang, Xianpeng Wang, Lixin Tang
