25 Result(s)
within
Yinnian He
Mathematical and Computational Engineering
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Article
Local tangential lifting virtual element method for the diffusion–reaction equation on the non-flat Voronoi discretized surface
In this paper, we propose the surface virtual element method (SVEM) combining with the local tangential lifting technique (LTL) to solve the diffusion–reaction (DR) equation on the non-flat Voronoi discretized...
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Article
A Stabilized Difference Finite Element Method for the 3D Steady Incompressible Navier-Stokes Equations
In this paper, we develop a stabilized difference finite element (SDFE) method for the 3D steady incompressible Navier-Stokes equations and apply Oseen iterative method to deal with the nonlinear term. Firstly...
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Article
Uniform Stability and Convergence with Respect to \((\nu , \mu , s, 1-\sigma )\) of the Three Iterative Finite Element Solutions for the 3D Steady MHD Equations
In this paper, the Stokes, Newton and Oseen iterative finite element methods are presented for the 3D steady MHD equations. These methods consist of approximating the solution pair ((u, B), p) of the 3D steady MH...
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Article
A Parallel Robin–Robin Domain Decomposition Method based on Modified Characteristic FEMs for the Time-Dependent Dual-porosity-Navier–Stokes Model with the Beavers–Joseph Interface Condition
In this paper, we propose and analyze the parallel Robin–Robin domain decomposition method based on the modified characteristic finite element method for the time-dependent dual-porosity-Navier–Stokes model wi...
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Article
Stability and Error Estimate of the Operator Splitting Method for the Phase Field Crystal Equation
In this paper, we propose a second-order fast explicit operator splitting method for the phase field crystal equation. The basic idea lied in our method is to split the original problem into linear and nonline...
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Article
A Discontinuous Galerkin Method for the Coupled Stokes and Darcy Problem
Combining the mixed discontinuous Galerkin method for the Darcy flow and the interior penalty discontinuous Galerkin methods for the Stokes problem, a locally conservative discrete scheme is proposed for numer...
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Article
A Posteriori Error Estimates for the Virtual Element Method for the Stokes Problem
This paper presents a residual-type a posteriori error estimator for the virtual element method for the Stokes problem. It is proved that the a posteriori error estimator is reliable and efficient. The virtual...
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Article
Two-Level Schwarz Methods for a Discontinuous Galerkin Approximation of Elliptic Problems with Jump Coefficients
We present two-level nonoverlap** and overlap** Schwarz preconditioners for the linear algebraic system arising from the weighted symmetric interior penalty Galerkin approximation of elliptic problems with...
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Article
Crank–Nicolson Leap-Frog Time Step** Decoupled Scheme for the Fluid–Fluid Interaction Problems
A fully discrete Crank-Nicolson leap-frog time step** decoupled (CNLFD) scheme is presented and studied for the fluid–fluid interaction problems. The proposed scheme deals with the spatial discretization by ...
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Article
Weak Galerkin Finite Element Methods for the Simulation of Single-Phase Flow in Fractured Porous Media
This paper presents a numerical simulation of the flow in fractured porous media, which can be efficiently described by the reduced model consisting of the bulk problem in the porous matrix and the fracture pr...
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Article
Two-Level Coupled and Decoupled Parallel Correction Methods for Stationary Incompressible Magnetohydrodynamics
In this paper, we propose two-level coupled correction and decoupled parallel correction finite element methods for solving the stationary magnetohydrodynamics (MHD) equations. We prove the error estimates for...
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Article
Two-Level Newton Iterative Method for the 2D/3D Stationary Incompressible Magnetohydrodynamics
In this paper, Newton iteration and two-level finite element algorithm are combined for solving numerically the stationary incompressible magnetohydrodynamics (MHD) under a strong uniqueness condition. The met...
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Article
\(H^2\) -Stability of the First Order Fully Discrete Schemes for the Time-Dependent Navier–Stokes Equations
This paper considers the \(H^2\) H 2 ...
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Article
Two-Level Newton’s Method for Nonlinear Elliptic PDEs
A combination method of Newton’s method and two-level piecewise linear finite element algorithm is applied for solving second-order nonlinear elliptic partial differential equations numerically. Newton’s metho...
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Article
Euler implicit/explicit iterative scheme for the stationary Navier–Stokes equations
In this paper, a new uniqueness assumption (A2) of the solution for the stationary Navier–Stokes equations is presented. Under assumption (A2), the exponential stability of the solution
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Article
A Family of Fourth-Order and Sixth-Order Compact Difference Schemes for the Three-Dimensional Poisson Equation
In this paper a family of fourth-order and sixth-order compact difference schemes for the three dimensional (3D) linear Poisson equation are derived in detail. By using finite volume (FV) method for derivation...
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Article
A stabilized multi-level method for non-singular finite volume solutions of the stationary 3D Navier–Stokes equations
This paper proposes and analyzes a stabilized multi-level finite volume method (FVM) for solving the stationary 3D Navier–Stokes equations by using the lowest equal-order finite element pair without relying on...
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Article
P 1-Nonconforming Quadrilateral Finite Volume Methods for the Semilinear Elliptic Equations
In this paper we use P 1-nonconforming quadrilateral finite volume methods with interpolated coefficients to solve the semilinear elliptic problems. Two types of control volumes are applied. Optim...
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Article
Newton Iterative Parallel Finite Element Algorithm for the Steady Navier-Stokes Equations
A combination method of the Newton iteration and parallel finite element algorithm is applied for solving the steady Navier-Stokes equations under the strong uniqueness condition. This algorithm is motivated b...
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Article
Local and parallel finite element algorithms for the stokes problem
Based on two-grid discretizations, some local and parallel finite element algorithms for the Stokes problem are proposed and analyzed in this paper. These algorithms are motivated by the observation that for a...
