  In this work is considered a diusion problem, referred to as the Ventcel
problem, involving a second order term on the domain boundary (the
Laplace-Beltrami operator). A variational formulation of the Ventcel problem is
studied, leading to a nite element discretization. The focus is on the
construction of high order curved meshes for the discretization of the physical
domain and on the denition of the lift operator, which is aimed to transform a
function dened on the mesh domain into a function dened on the physical one.
This lift is dened in a way as to satisfy adapted properties on the boundary,
relatively to the trace operator. Error estimations are computed and expressed
both in terms of nite element approximation error and of geometrical error,
respectively associated to the nite element degree k $\ge$ 1 and to the mesh
order r $\ge$ 1. The numerical experiments we led allow us to validate the
results obtained and proved on the a priori error estimates depending on the
two parameters k and r.
