Linear Advection with Ill-Posed Boundary Conditions via $L^1$-Minimization

Linear Advection with Ill-Posed Boundary Conditions via $L^1$-Minimization

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.

Author Details

Jean-Luc Guermond

Bojan Popov