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Title of Journal: Numer Math

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Abbravation: Numerische Mathematik

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Springer-Verlag

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DOI

10.1016/j.abb.2015.01.007

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0945-3245

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Multilevel spectral galerkin method for the navie

Authors: Yinnian He KamMoon Liu Weiwei Sun
Publish Date: 2005/07/25
Volume: 101, Issue: 3, Pages: 501-522
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Abstract

A multilevel spectral Galerkin method for the twodimensional nonstationary NavierStokes equations is presented The method proposed here is a multiscale method in which the fully nonlinear NavierStokes equations are solved only on a lowdimensional space Open image in new window subsequent approximations are generated on a succession of higherdimensional spaces Open image in new window j=2 J by solving a linearized NavierStokes problem around the solution on the previous level Error estimates depending on the kinematic viscosity 0ν1 are also presented for the Jlevel spectral Galerkin method The optimal accuracy is achieved when Open image in new window We demonstrate theoretically that the Jlevel spectral Galerkin method is much more efficient than the standard onelevel spectral Galerkin method on the highestdimensional space Open image in new window The work of this author was supported in part by the NSF of China 10371095 City University of Hong Kong Research Project 7001093 Hong Kong and the Research Grants Council of the Hong Kong Special Administrative Region China Project No CityU 1084/02P

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  2. A new class of symplectic integration schemes based on generating functions
  3. An optimal adaptive finite element method for elastoplasticity
  4. Galerkin and Runge–Kutta methods: unified formulation, a posteriori error estimates and nodal superconvergence
  5. Controllability of an Elliptic equation and its Finite Difference Approximation by the Shape of the Domain
  6. Decay rates of adaptive finite elements with Dörfler marking
  7. Multi-parameter regularization and its numerical realization
  8. Spectral conditions for admissibility and observability of wave systems: applications to finite element schemes
  9. Convergence of a semiclassical wavepacket based time-splitting for the Schrödinger equation
  10. A uniformly stable Fortin operator for the Taylor–Hood element
  11. A locking-free $$hp$$ DPG method for linear elasticity with symmetric stresses
  12. Pathwise approximation of stochastic differential equations on domains: higher order convergence rates without global Lipschitz coefficients
  13. The multi-level Monte Carlo finite element method for a stochastic Brinkman Problem
  14. Explicit trace inequalities for isogeometric analysis and parametric hexahedral finite elements
  15. Hölder estimates for Green’s functions on convex polyhedral domains and their applications to finite element methods
  16. A residual–based error estimator for BEM–discretizations of contact problems
  17. An adaptive anisotropic perfectly matched layer method for 3-D time harmonic electromagnetic scattering problems
  18. Preconditioners for pseudodifferential equations on the sphere with radial basis functions
  19. Symmetric multistep methods for constrained Hamiltonian systems
  20. Discrete minimum and maximum principles for finite element approximations of non-monotone elliptic equations
  21. Numerical Eulerian method for linearized gas dynamics in the high frequency regime
  22. Proper generalized decomposition for nonlinear convex problems in tensor Banach spaces
  23. The boundary element spline collocation for nonuniform meshes on the torus
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  26. On generalized successive overrelaxation methods for augmented linear systems
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  28. A mixed finite element method for nonlinear elasticity: two-fold saddle point approach and a-posteriori error estimate
  29. Intrinsic representation of tangent vectors and vector transports on matrix manifolds
  30. Crouzeix–Raviart boundary elements
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