On a 2D vector Poisson problem with apparently mutually exclusive scalar boundary conditions

This work is devoted to the study of a two-dimensional vector Poisson equat ion with the normal component of the unknown and the value of the divergenc e of the unknown prescribed simultaneously on the entire boundary. These tw o scalar boundary conditions appear prima facie alternative in a standard v ariational framework. An original variational formulation of this boundary value problem is proposed here. Furthermore; an uncoupled solution algorith m is introduced together with its finite element approximation. The numeric al scheme has been implemented and applied to solve a simple test problem. Mathematics Subject Classification. 35J20, 35Q, 65N30, 76.