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Volume 2, Issue 3
Nonstandard Nonconforming Approximation of the Stokes Problem, I: Periodic Boundary Conditions

J.-L. Guermond

Int. J. Numer. Anal. Mod., 2 (2005), pp. 345-354.

Published online: 2005-02

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  • Abstract

This paper analyzes a nonstandard form of the Stokes problem where the mass conservation equation is expressed in the form of a Poisson equation for the pressure. This problem is shown to be well-posed in the $d$-dimensional torus. A nonconforming approximation is proposed and, contrary to what happens when using the standard saddle-point formulation, the proposed setting is shown to yield optimal convergence for every pairs of approximation spaces.

  • Keywords

Stokes equations, finite elements, nonconforming approximation, incompressible flows and Poisson equation.

  • AMS Subject Headings

65N30, 35Q30, 76D07

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{IJNAM-2-345, author = {Guermond , J.-L.}, title = {Nonstandard Nonconforming Approximation of the Stokes Problem, I: Periodic Boundary Conditions}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2005}, volume = {2}, number = {3}, pages = {345--354}, abstract = {

This paper analyzes a nonstandard form of the Stokes problem where the mass conservation equation is expressed in the form of a Poisson equation for the pressure. This problem is shown to be well-posed in the $d$-dimensional torus. A nonconforming approximation is proposed and, contrary to what happens when using the standard saddle-point formulation, the proposed setting is shown to yield optimal convergence for every pairs of approximation spaces.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/935.html} }
TY - JOUR T1 - Nonstandard Nonconforming Approximation of the Stokes Problem, I: Periodic Boundary Conditions AU - Guermond , J.-L. JO - International Journal of Numerical Analysis and Modeling VL - 3 SP - 345 EP - 354 PY - 2005 DA - 2005/02 SN - 2 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/935.html KW - Stokes equations, finite elements, nonconforming approximation, incompressible flows and Poisson equation. AB -

This paper analyzes a nonstandard form of the Stokes problem where the mass conservation equation is expressed in the form of a Poisson equation for the pressure. This problem is shown to be well-posed in the $d$-dimensional torus. A nonconforming approximation is proposed and, contrary to what happens when using the standard saddle-point formulation, the proposed setting is shown to yield optimal convergence for every pairs of approximation spaces.

Guermond , J.-L.. (2005). Nonstandard Nonconforming Approximation of the Stokes Problem, I: Periodic Boundary Conditions. International Journal of Numerical Analysis and Modeling. 2 (3). 345-354. doi:
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