Pointwise convergence rate of vanishing viscosity approximations for scalar conservation laws with boundary

This article is concerned with the pointwise error estimates for vanishing viscosity approximations to scalar convex conservation laws with boundary. By the weighted error function and a bootstrap extrapolation technique introduced by Tadmor-Tang, an optimal pointwise convergence rate is derived for the vanishing viscosity approximations to the initial-boundary value problem for scalar convex conservation laws, whose weak entropy solution is piecewise C2-smooth with interaction of elementary waves and the boundary. The analysis method in this article can be used to deal with the case in which the piecewise smooth solutions of inviscid have finitely many waves with possible all kinds of interaction with the boundary.