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 - <p style="text-align: justify;">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.</p>