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Publication 03-CNA-05
Convergence of the Discontinuous Galerkin Method
for Discontinuous Solutions Noel J. Walkington Abstract We consider linear first order scalar equations of the form with appropriate initial and boundary conditions. It is shown that approximate solutions computed using the discontinuos Galerkin method will converge in when the coefficients and and data satisfy the minimal asusmptions required to establish existence and uniqueness of solutions. In particular, 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 |