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Article
A Voigt regularization of the thermally coupled magnetohydrodynamic flow
We prove existence and uniqueness of weak solution to a Voigt regularization of the three-dimensional thermally coupled MHD equations. Moreover, for the considered equations, we propose a fully discrete scheme...
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Article
Optimal error estimates of penalty difference finite element method for the 3D steady Navier-Stokes equations
In this paper, a penalty difference finite element (PDFE) method is presented for the 3D steady Navier-Stokes equations by using the finite element space pair ...
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Article
A second-order scheme based on blended BDF for the incompressible MHD system
For the incompressible MHD equations, we present a fully discrete second-order-in-time scheme based on a blended BDF and extrapolation treatments for nonlinear terms. The proposed scheme is more accurate than ...
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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
A divergence-free weak virtual element method for the Navier-Stokes equation on polygonal meshes
In this paper, we present a divergence-free weak virtual element method for the Navier-Stokes equation on polygonal meshes. The velocity and the pressure are discretized by the H(div) virtual element and disconti...
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Article
Two robust virtual element methods for the Brinkman equations
In this paper, we present two stable virtual element methods for the Brinkman equations robust in the Stokes and Darcy limits. We use a pair of stable virtual elements for the velocity and pressure. Firstly, w...
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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
An Uzawa-type algorithm for the coupled Stokes equations
An Uzawa-type algorithm is designed for the coupled Stokes equations discretized by the mixed finite element method. The velocity solved by the presented algorithm is weakly divergence-free, which is different...
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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
Regularity results of solution uniform in time for complex Ginzburg-Landau equation
We provide the H2-regularity result of the solution ψ and its first-order time derivative ψt and the second-order time derivative ψtt for the complex Ginzburg-Landau equation with the Dirichlet or Neumann boundar...
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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
Local and parallel finite element algorithm based on the partition of unity method for the incompressible MHD flow
Based on the partition of unity method (PUM), a local and parallel finite element method is designed and analyzed for solving the stationary incompressible magnetohydrodynamics (MHD). The key idea of the propo...
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Article
Convergence of some finite element iterative methods related to different Reynolds numbers for the 2D/3D stationary incompressible magnetohydrodynamics
Based on finite element method (FEM), some iterative methods related to different Reynolds numbers are designed and analyzed for solving the 2D/3D stationary incompressible magnetohydrodynamics (MHD) numerical...
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Article
An efficient two-step algorithm for the incompressible flow problem
A new two-step stabilized finite element method for the 2D/3D stationary Navier–Stokes equations based on local Gauss integration is introduced and analyzed in this paper. The method consists of solving one Na...
