On the Treatment of Bounded Domains and Boundary Conditions in Adaptive Wavelet Methods

Angela \AU{Kunoth
RWTH Aachen, Germany


For the numerical solution of elliptic partial differential equations, embedding the domain into a larger simple one, called fictitious domain, has been a favorable method, in particular, for domains with complicated boundaries. This approach in combination with the idea of explicitly treating essential boundary conditions by means of Lagrange multipliers decouples the differential operator from the boundary conditions as much as possible. In a weak saddle point formulation of the problem, stable discretizations on the domain and the boundary are then enforced by the corresponding Ladysenskaja-Babuska-Brezzi (LBB) condition.

In my talk, I would like to present some new ideas how to use an adaptive wavelet-based method for this saddle point problem combined with a strategy how to satisfy the LBB condition for the problem at hand.