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Publication 02-CNA-015
Noel J. Walkington Abstract: We consider linear first order scalar equations of the form
$\rho_t +
div(\rho v) + a \rho = f$ with appropriate initial and boundary
conditions. It is shown that approximate solutions computed using the
Galerkin method will converge in
$L^2[0,T;L^2((\Omega)]$ when the
coefficients $v$ and $a$ and data $f$ satisfy the minimal assumptions required to establish existence and uniqueness of solutions. In particular,
$v$ need not be Lipschitz, so characteristics of the equation may not be defined, and the solutions being approximated may not have bounded variation.Get the paper in its entirety as 02-CNA-015.pdf |