TY - JOUR
T1 - Linear Advection with Ill-Posed Boundary Conditions via $L^1$-Minimization
AU - Guermond , Jean-Luc
AU - Popov , Bojan
JO - International Journal of Numerical Analysis and Modeling
VL - 1
SP - 39
EP - 47
PY - 2007
DA - 2007/04
SN - 4
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/ijnam/849.html
KW - finite elements, best $L^1$-approximation, viscosity solution, linear transport, ill-posed problem.
AB - <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>