Existence, uniqueness, and computation of solutions for mixed problems in compressible fluid flow
Initial-boundary value problems are considered for the one-dimensional Navier-Stokes equations for compressible flow on a finite interval. Convergence of finite difference schemes are proved for each of three different cases of initial and boundary data. For BV discontinuous initial data that is piecewise smooth the density is shown to remain discontinuous and a bound is given for the error of an approximate solution in a norm that dominates the sup-norm of the density. For \(H^ 1\) initial data a different error bound is given in the same norm.
convergence of finite difference schemes
scientific article; zbMATH DE number 168003