Linear advection with ill-posed boundary conditions via L-1-minimization

It is proven that in dimension one the piecewise linear best L1-approximation to the linear transport equation equipped with a set of ill-posed boundary conditions converges in Wloc1,1 to the viscosity solution of the equation and the boundary layer associated with the ill-posed boundary condition is always localized in one mesh cell, i.e., the "last" one. 2007 Institute for Scientific Computing and Information.

Linear advection with ill-posed boundary conditions via L-1-minimization Academic Article