Displaying similar documents to “Spectral element discretization of the vorticity, velocity and pressure formulation of the Stokes problem”

Spectral discretization of Darcy equations coupled with Navier-Stokes equations by vorticity-velocity-pressure formulation

Yassine Mabrouki, Jamil Satouri (2022)

Applications of Mathematics

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We consider a model coupling the Darcy equations in a porous medium with the Navier-Stokes equations in the cracks, for which the coupling is provided by the pressure's continuity on the interface. We discretize the coupled problem by the spectral element method combined with a nonoverlapping domain decomposition method. We prove the existence of solution for the discrete problem and establish an error estimation. We conclude with some numerical tests confirming the results of our analysis. ...

A new formulation of the Stokes problem in a cylinder, and its spectral discretization

Nehla Abdellatif, Christine Bernardi (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

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We analyze a new formulation of the Stokes equations in three-dimensional axisymmetric geometries, relying on Fourier expansion with respect to the angular variable: the problem for each Fourier coefficient is two-dimensional and has six scalar unknowns, corresponding to the vector potential and the vorticity. A spectral discretization is built on this formulation, which leads to an exactly divergence-free discrete velocity. We prove optimal error estimates.

A penalty method for the time-dependent Stokes problem with the slip boundary condition and its finite element approximation

Guanyu Zhou, Takahito Kashiwabara, Issei Oikawa (2017)

Applications of Mathematics

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We consider the finite element method for the time-dependent Stokes problem with the slip boundary condition in a smooth domain. To avoid a variational crime of numerical computation, a penalty method is introduced, which also facilitates the numerical implementation. For the continuous problem, the convergence of the penalty method is investigated. Then we study the fully discretized finite element approximations for the penalty method with the P1/P1-stabilization or P1b/P1 element....

A splitting method using discontinuous Galerkin for the transient incompressible Navier-Stokes equations

Vivette Girault, Béatrice Rivière, Mary F. Wheeler (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

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In this paper we solve the time-dependent incompressible Navier-Stokes equations by splitting the non-linearity and incompressibility, and using discontinuous or continuous finite element methods in space. We prove optimal error estimates for the velocity and suboptimal estimates for the pressure. We present some numerical experiments.