Error estimates for spectral approximation of linear advection equations over an hypercube (Q2266363)

Considered is the equation \(u_ t+div(\vec au)+bu=f\) with initial conditions, and with first kind homogeneous conditions on inflow boundaries. Some embedding theorems in weighted Sobolev spaces and a stability estimate implying uniqueness of the solution are proved. The dependence on the spatial coordinates is discretized by a polynomially based Galerkin method and by collocation. In both cases error estimates are obtained showing convergence with an order depending on the regularity of the solution.