Year: 2007
Author: Jean-Luc Guermond, Bojan Popov
International Journal of Numerical Analysis and Modeling, Vol. 4 (2007), Iss. 1 : pp. 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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2007-IJNAM-849
International Journal of Numerical Analysis and Modeling, Vol. 4 (2007), Iss. 1 : pp. 39–47
Published online: 2007-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 9
Keywords: finite elements best $L^1$-approximation viscosity solution linear transport ill-posed problem.