@Article{IJNAM-4-39,
author = {Guermond , Jean-Luc and Popov , Bojan},
title = {Linear Advection with Ill-Posed Boundary Conditions via $L^1$-Minimization},
journal = {International Journal of Numerical Analysis and Modeling},
year = {2007},
volume = {4},
number = {1},
pages = {39--47},
abstract = {<p style="text-align: justify;">It is proven that in dimension one the piecewise linear best $L^1$-approximation to the linear transport equation equipped with a set
of ill-posed boundary conditions converges in $W_{loc}^{1,1}$ 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 &quot;last&quot; one.</p>},
issn = {2617-8710},
doi = {https://doi.org/},
url = {http://global-sci.org/intro/article_detail/ijnam/849.html}
}