Finite element framework for closest point projection method for surface PDEs

We present a class of weak problem statemets which natural approximation using finite element method leads to finite element version of the closest point projection method for surface PDEs Substantial attention is paid to variationally consistent treatment of Dirichlet boundary conditions using closest point projection approach.We consider convential 2D problem settings as well as their generalization to the case of an arbitrary sufficiently smooth surfaces embedded into 3D space.