@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 = {

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 "last" one.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/849.html} }