Curved finite element methods for the solution of singular integral equations on surfaces in R3

We have shown in 1]that the singular integral equation (1.2) on a closed surface Γ of R³ admits a unique solution q and is variational and coercive in the Hilbert space $\text{H}{}^{\mathrm{<mtext>?</mtext><mtext>1</mtext><mtext>2</mtext>}}$(Γ). In this paper, with the help of curved finite elements, we introduce an approximate surface Γ_h, and an approximate problem on Γ_h, whose solution is q_h. Then we study the error of approximation |q ? q_h| in some Hubert spaces and also the associated error |u ? u_h| of the potential.