Local and parallel finite element algorithm based on the partition of unity for incompressible flows

DOI10.1007/s10915-014-9979-xzbMath1327.65249OpenAlexW2032636202MaRDI QIDQ898492

Feng Shi, Haibiao Zheng, Jia-ping Yu

Publication date: 9 December 2015

Published in: Journal of Scientific Computing (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10915-014-9979-x

zbMATH Keywords

incompressible flowspartition of unityoversamplinglocal and parallel

Mathematics Subject Classification ID

Stokes and related (Oseen, etc.) flows (76D07) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Finite element methods applied to problems in fluid mechanics (76M10) Multigrid methods; domain decomposition for initial value and initial-boundary value problems involving PDEs (65M55)

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Uses Software

• FreeFem++
• SG

Cites Work

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• Adaptive local postprocessing finite element method for the Navier-Stokes equations
• A parallel Oseen-linearized algorithm for the stationary Navier-Stokes equations
• Newton iterative parallel finite element algorithm for the steady Navier-Stokes equations
• A finite element variational multiscale method for incompressible flows based on two local Gauss integrations
• The partition of unity parallel finite element algorithm
• Local and parallel finite element algorithms for the Stokes problem
• Finite element methods (Part 1)
• Nonlinear Galerkin methods and mixed finite elements: Two-grid algorithms for the Navier-Stokes equations
• The partition of unity finite element method: basic theory and applications
• High-Re solutions for incompressible flow using the Navier-Stokes equations and a multigrid method
• A defect-correction method for the incompressible Navier-Stokes equations.
• A New Paradigm for Parallel Adaptive Meshing Algorithms
• Local and Parallel Finite Element Algorithms Based on the Partition of Unity for the Stokes Problem
• Partition of unity refinement for local approximation
• Postprocessing Fourier Galerkin Method for the Navier–Stokes Equations
• Finite Element Methods for Navier-Stokes Equations
• Numerical Solution of the Stationary Navier--Stokes Equations Using a Multilevel Finite Element Method
• STABILITY OF HIGHER ORDER TRIANGULAR HOOD-TAYLOR METHODS FOR THE STATIONARY STOKES EQUATIONS
• Three-Dimensional Finite Element Methods for the Stokes Problem
• THE PARTITION OF UNITY METHOD
• A New Paradigm for Parallel Adaptive Meshing Algorithms
• A conforming finite element method for overlapping and nonmatching grids
• Error Estimates on a New Nonlinear Galerkin Method Based on Two-Grid Finite Elements
• Local and parallel finite element algorithms based on two-grid discretizations
• A Finite Element Variational Multiscale Method for the Navier--Stokes Equations
• An AIM and one-step Newton method for the Navier-Stokes equations
• Adaptive numerical treatment of elliptic systems on manifolds