Vorticity–velocity-pressure and stream function-vorticity formulations for the Stokes problem

Spectral element discretization of the vorticity, velocity and pressure formulation of the Stokes problem

“…It is readily checked that the kernel 13) coincides with the space of divergence-free functions in D(Ω). Similarly, the kernel 14) coincides with the space of pairs (ϑ, w) in H 0 (curl, Ω) × V such that ϑ is equal to curl w in the distribution sense. We observe that, for any solution (ω, u, p) of problem (2.9), the pair (ω, u) is a solution of the following reduced problem:…”

“…It maps smooth functions in H(curl, Ω k ) onto the space C k N defined in (3.2) and satisfies, for all functions 14) and, for all functions ϕ in H(curl,…”

A priori and a posteriori estimates for three‐dimensional Stokes equations with nonstandard boundary conditions

“…We refer also to Girault's work [16] for a vector potential-vorticity approximation of similar Navier-Stokes type problems and to [15] for the steady-state incompressible Navier-Stokes equations with non standard boundary conditions. For the Vorticity-velocity-pressure formulation for the Stokes problem, we refer to [10], [11] and [28]. We also refer to [24] where Repin establishes a posteriori estimates for the velocity, stress and pressure fields for the stationary Stokes problem and where his approach is based on duality theory of the calculus of variations.…”

Error studies of the Coupling Darcy-Stokes System with velocity-pressure formulation

“…For the Vorticity-velocity-pressure formulation for the Stokes problem, we refer to [10], [11] and [20]. For the coupling problem, we cite the works [2], [3], [8], [9], [16] and [21].…”