Asymptotic analysis of an ε-Stokes problem with Dirichlet boundary conditions

In this thesis, we propose an ε-Stokes problem connecting the Stokes problem and the corresponding pressure-Poisson equation using one pa- rameter ε > 0. We prove that the solution to the ε-Stokes problem, converges as ε tends to 0 or ∞ to the Stokes and pressure-Poisson prob- lem, respectively. Most of these results are new. The precise statements of the new results are given in Proposition 3.5, Theorem 4.1, Theorem 5.2, and Theorem 5.3. Numerical results illustrating our mathematical results are also presented.