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In this work is considered a diusion problem, referred to as the Ventcelproblem, involving a second order term on the domain boundary (theLaplace-Beltrami operator). A variational formulation of the Ventcel problem isstudied, leading to a nite element discretization. The focus is on theconstruction of high order curved meshes for the discretization of the physicaldomain and on the denition of the lift operator, which is aimed to transform afunction 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 expressedboth in terms of nite element approximation error and of geometrical error,respectively associated to the nite element degree k $\ge$ 1 and to the meshorder r $\ge$ 1. The numerical experiments we led allow us to validate theresults obtained and proved on the a priori error estimates depending on thetwo parameters k and r.

A priori error estimates of a diusion equation with Ventcel boundary conditions on curved meshes