L^∞-Stable Approximation of a Solution to Div(Y) = f for $f\in L^2$ in Two Dimensions

In this paper, we propose a numerical approach for the derivation of a stable approximation in L $^\infty$-norm of a solution to div(Y) = f for $f\in L^2$ in two dimensions. The derivation of this result is based on preliminary stability results in Fourier approximationtheory that are interesting by themselves. Numerical simulation sustain the proof of the theorem.