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Article
A Parallel Finite Element Discretization Scheme for the Natural Convection Equations
This article presents a parallel finite element discretization scheme for solving numerically the steady natural convection equations, where a fully overlap** domain decomposition technique is used for paral...
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Article
Analysis of a Parallel Grad-Div Stabilized Method for the Navier–Stokes Problem with Friction Boundary Conditions
By combining grad-div stabilization used for improving pressure-robustness and full domain partition used for parallelization, a new parallel finite element method for the steady Navier–Stokes problem with fri...
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Article
A Parallel Finite Element Discretization Algorithm Based on Grad-Div Stabilization for the Navier–Stokes Equations
We present and study a parallel grad-div stabilized finite element discretization algorithm based on entire-overlap** domain decomposition for the numerical simulation of Navier–Stokes equations. The algorit...
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Article
A parallel two-grid method based on finite element approximations for the 2D/3D Navier–Stokes equations with dam**
Based on two-grid discretizations, this paper introduces a parallel finite element method for the 2D/3D Navier–Stokes equations with dam**. In this method, we first solve a fully nonlinear problem on a globa...
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Article
A three-step defect-correction stabilized algorithm for incompressible flows with non-homogeneous Dirichlet boundary conditions
Based on two-grid discretizations and quadratic equal-order finite elements for the velocity and pressure approximations, we develop a three-step defect-correction stabilized algorithm for the incompressible N...
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Article
A New Two-grid Algorithm Based on Newton Iteration for the Stationary Navier–Stokes Equations with Dam**
Based on finite element discretization, a new two-grid algorithm based on Newton iteration is proposed to solve the stationary Navier–Stokes equations with nonlinear dam** term. The proposed new two-grid alg...
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Article
A three-step defect-correction algorithm for incompressible flows with friction boundary conditions
Based on finite element discretization and a recent variational multiscale-stabilized method, we propose a three-step defect-correction algorithm for solving the stationary incompressible Navier-Stokes equatio...
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Article
Stability and convergence of some parallel iterative subgrid stabilized algorithms for the steady Navier-Stokes equations
Based on finite element discretization and a fully overlap** domain decomposition, we propose and study some parallel iterative subgrid stabilized algorithms for the simulation of the steady Navier-Stokes eq...
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Article
Local and parallel finite element algorithms for the time-dependent Oseen equations
Based on two-grid discretizations, local and parallel finite element algorithms are proposed and analyzed for the time-dependent Oseen equations. Using conforming finite element pairs for the spatial discretiz...
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Article
Parallel iterative stabilized finite element methods based on the quadratic equal-order elements for incompressible flows
Combining the quadratic equal-order stabilized method with the approach of local and parallel finite element computations and classical iterative methods for the discretization of the steady-state Navier–Stoke...
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Article
A parallel stabilized finite element method based on the lowest equal-order elements for incompressible flows
Based on a fully overlap** domain decomposition technique, a parallel stabilized equal-order finite element method for the steady Stokes equations is presented and studied. In this method, each processor com...
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Article
A two-level fully discrete finite element variational multiscale method for the unsteady Navier–Stokes equations
A two-level fully discrete finite element variational multiscale method based on two local Gauss integrations for the unsteady Navier–Stokes equations is presented and studied, where conforming finite element ...
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Article
A second-order finite element variational multiscale scheme for the fully discrete unsteady Navier–Stokes equations
In this report, we present and study a fully discrete finite element variational multiscale scheme for the unsteady incompressible Navier–Stokes equations where high Reynolds numbers are allowed. The scheme us...
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Article
A three-step Oseen correction method for the steady Navier–Stokes equations
We present and analyze a two-grid scheme based on mixed finite element approximations for the steady incompressible Navier–Stokes equations. This numerical scheme aims at the simulations of high Reynolds numbe...
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Article
A Parallel Subgrid Stabilized Finite Element Method Based on Two-Grid Discretization for Simulation of 2D/3D Steady Incompressible Flows
Based on domain decomposition and two-grid discretization, a parallel subgrid stabilized finite element method for simulation of 2D/3D steady convection dominated incompressible flows is proposed and analyzed....
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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 based on two-grid discretizations for the transient Stokes equations
Based on two-grid discretizations, some local and parallel finite element algorithms for the d-dimensional (d = 2,3) transient Stokes equations are proposed and analyzed. Both semi- and fully discrete schemes are...
