Article
Mathematics
Jing Han, Guangzhi Du
Summary: In this article, two kinds of local and parallel stabilized finite element methods for the Stokes-Darcy model are proposed and investigated. The algorithms approximate the velocity, pressure, and piezometric head using the lowest equal-order finite element pairs (P1-P1-P1). By introducing a stabilized term and the technique of partition of unity, the algorithms overcome the inf-sup condition and achieve valid and efficient results.
Article
Mathematics, Applied
Guangzhi Du, Liyun Zuo, Yuhong Zhang
Summary: In this paper, a new local and parallel finite element method is presented and studied for the coupled Stokes-Darcy model, based on two-grid discretizations and superposition principle. By using the superposition principle to generate a series of local and independent subproblems, a global continuous approximation is obtained, and optimal error estimates are derived. Numerical results are reported to support the theoretical findings.
JOURNAL OF SCIENTIFIC COMPUTING
(2022)
Article
Mathematics, Applied
Guangzhi Du, Liyun Zuo
Summary: In this paper, a local and parallel partition of unity scheme is proposed for the mixed Navier-Stokes-Darcy problem. The method combines the two-grid method with a partition of unity and exhibits several advantageous features, including parallel computing and optimal error bounds. The convergence of the method is also proven and numerical experiments are conducted to validate the theoretical results.
NUMERICAL ALGORITHMS
(2022)
Article
Mathematics
Abdumauvlen Berdyshev, Dossan Baigereyev, Kulzhamila Boranbek
Summary: This paper aims at efficiently implementing the fractional-order generalization of the stochastic Stokes-Darcy model, which has significant scientific, applied, and economic importance in hydrology, the oil industry, and biomedicine. The paper proposes an efficient numerical method based on a higher-order approximation formula for the fractional derivative, higher-order finite difference relations, and a finite element approximation in the spatial direction. The stability and convergence of the method are rigorously analyzed and confirmed by computational experiments. The method is also applied to implementing the fractional-order stochastic Stokes-Darcy model using an ensemble technique and parallel threads for evaluating discrete fractional derivatives, showing its efficiency in numerical tests.
Article
Mathematics, Applied
Xinhui Wang, Guangzhi Du, Liyun Zuo
Summary: A new local and parallel finite element method based on two-grid discretization is proposed and investigated for the mixed Navier-Stokes-Darcy problem. The method considers partition of unity method to generate local subproblems and achieves global continuous approximations. Theoretical analysis and numerical tests are conducted to support the proposed method.
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2021)
Article
Mathematics, Applied
Xinhui Wang, Guangzhi Du, Yi Li
Summary: In this paper, a modified local and parallel finite element method (MLPFEM) is proposed for the coupled Stokes-Darcy problem. The method combines a partition of unity with backtracking technique to improve computational efficiency while maintaining global continuity, and achieves optimal error bounds.
NUMERICAL ALGORITHMS
(2023)
Article
Mathematics, Applied
Xinhui Wang, Guangzhi Du
Summary: In this paper, local and parallel stabilized finite element methods based on two-grid discretizations are proposed and investigated for the Stokes problem. The lowest equal-order finite element pairs are chosen to circumvent the discrete inf-sup condition in the finite element discretization. These algorithms derive the low-frequency components of the solution on a coarse grid and capture the high-frequency components on a fine grid using local and parallel procedures. Optimal error bounds are demonstrated and numerical experiments support the theoretical results.
NUMERICAL ALGORITHMS
(2023)
Article
Mathematics, Applied
Yanren Hou, Dandan Xue
Summary: This paper investigates a two-grid decoupling finite element scheme for the mixed Navier-Stokes/Darcy model with Beavers-Joseph-Saffman's interface condition and establishes the optimal error estimate for the approximate solution. The analysis shows that the fine grid decoupled problems, i.e., the Navier-Stokes equations and the Darcy equation, can be solved simultaneously and achieve the optimal convergence order.
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2022)
Article
Mathematics, Applied
Yali Gao, Rui Li, Xiaoming He, Yanping Lin
Summary: A fully decoupled, linearized, and unconditionally stable finite element method is developed to solve the Cahn-Hilliard-Navier-Stokes-Darcy model in the coupled free fluid region and porous medium region. By introducing two auxiliary energy variables, the equivalent system that is consistent with the original system is derived. The study presents a coupled linearized time-stepping method to solve the reformulated system and proves its unconditionally energy stability. Further computational efficiency is achieved through special treatment for interface conditions and the use of an artificial compression approach to decouple the subdomains and the Navier-Stokes equation.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2024)
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
Nan Jiang, Changxin Qiu
Summary: This paper proposes an efficient algorithm for fast computation of a set of realizations of the stochastic Stokes-Darcy model. The algorithm only requires solving two linear systems with the same constant coefficient matrices, and stability and convergence analysis have been conducted. Numerical experiments support theoretical results and demonstrate the application of the method.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2022)
Article
Engineering, Multidisciplinary
Houbiao Ma, Yahui Zhang
Summary: In this study, a novel efficient 3D vibro-acoustic analysis method, PUFEM-FEM, is proposed, which can analyze multiple frequencies without the need for repeated meshing, while retaining the FEM's ability to model complex structures in great detail.
ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS
(2022)
Article
Mathematics, Applied
Qingtao Li, Guangzhi Du
Summary: This paper proposes and investigates some local and parallel finite element methods based on two-grid discretizations for a non-stationary coupled Stokes-Darcy model. By utilizing coarse grid to approximate the mixed model and solving the residual equations on fine grid, the decoupling and global continuous approximation are achieved.
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2022)
Article
Computer Science, Interdisciplinary Applications
P. Destuynder, L. Hervella-Nieto, P. M. Lopez-Perez, J. Orellana, A. Prieto
Summary: In this study, the time harmonic propagation of elastic waves in layered media is numerically simulated using a modal-based PUFEM approach, which utilizes tensor-product expressions of eigenmodes to fulfill coupling conditions among layers, avoiding quadrature errors. The reliability of the method is validated through various test scenarios, highlighting the importance of selecting a suitable discrete PUFEM basis for crack observability on coupling boundaries.
COMPUTERS & STRUCTURES
(2022)
Article
Computer Science, Interdisciplinary Applications
Yali Gao, Daozhi Han, Xiaoming He, Ulrich Ruede
Summary: In this article, numerical modeling and simulation of coupled two-phase free flow and two-phase porous media flow using the phase field approach are considered. Unconditionally stable finite element methods and time stepping methods are proposed to efficiently solve the coupled model and preserve the energy law. Numerical experiments demonstrate the convergence and energy-law preserving properties of the proposed methods.
JOURNAL OF COMPUTATIONAL PHYSICS
(2022)
