Pointwise Error Estimates Of Vanishing Viscosity Methods For Initial-boundary Value Problems For Scalar Conservation Laws

This thesis is concerned with the pointwise error estimates of vanishing viscosity methods for initial-boundary value problems for scalar convex conservation laws. By using the weighted error function and a bootstrap extrapolation technique introduced by Tadmor-Tang, we derive the optimal pointwise error estimate that is O(ε) for scalar convex conservation laws whose initial-boundary data are a finite number of piecewise constant with strictly decreasing initial data and increasing boundary data respectively.