An up-wind finite element method for a filtration problem
The notion of non-orthogonal multi-resolution analysis and its compatibility with differentiation (as expressed by the commutation formula) lead us to the construction of a multi-resolution analysis of L2(Rn)n which is well adapted to the approximation of divergence-free vector functions. Thus, we obtain unconditional bases of compactly supported divergence-free vector wavelets.
Let be a Banach space with a countable unconditional basis (e.g., ), an open set and complex-valued holomorphic functions on , such that the Fréchet differentials are linearly independant over at each . We suppose that is a complete intersection and we consider a holomorphic Banach vector bundle . If (resp.) denote the ideal of germs of holomorphic functions on that vanish on (resp. the sheaf of germs of holomorphic sections of ), then the sheaf cohomology groups , vanish...