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Publication 02-CNA-015

Convergence of the Discontinuous Galerkin Method for Discontinuous Solutions

Noel J. Walkington
Department of Mathematical Sciences
Carnegie Mellon University
Pittsburgh, PA 15213

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

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