We recall the origin of lattice Boltzmann scheme and detail the version due to D\textquotesingle Humières [8]. We present a formal analysis of this lattice Boltzmann scheme in terms of a single numerical infinitesimal parameter. We derive third order equivalent partial differential equation of this scheme. Both situations of single conservation law and fluid flow with mass and momentum conservations are detailed. We apply our analysis to so-called D1Q3 and D2Q9 lattice Boltzmann schemes in one and two space dimensions.