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Publication 03-CNA-005
Noel J. Walkington Abstract: We consider linear first order scalar
equations of the form
$p_t + div(pv)+ap=f$ with appropriate initial and boundary conditions. It is shown that approximate solutions
computed using the discontinuos Galerkin method will converge in
$L^2[0,T;L^2(\Omega)]$ when the coefficients $v$ and $a$ and data
$f$ satisfy the minimal asusmptions 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 03-CNA-005.pdf |