Mathematical and numerical analysis of a simplified time-dependent viscoelastic flow
Bonito, Andrea ; Clément, Philippe ; Picasso, Marco
In: Numerische Mathematik, 2007, vol. 107, no. 2, p. 213-255
Ajouter à la liste personnelle- Summary
- A time-dependent model corresponding to an Oldroyd-B viscoelastic fluid is considered, the convective terms being disregarded. Global existence in time is proved in Banach spaces provided the data are small enough, using the implicit function theorem and a maximum regularity property for a three fields Stokes problem. A finite element discretization in space is then proposed. Existence of the numerical solution is proved for small data, so as a priori error estimates, using again an implicit function theorem