Center for                           Nonlinear Analysis CNA Home People Seminars Publications Workshops and Conferences CNA Working Groups CNA Comments Form Summer Schools Summer Undergraduate Institute PIRE Cooperation Graduate Topics Courses SIAM Chapter Seminar Positions Contact Publication 02-CNA-015 Convergence of the Discontinuous Galerkin Method for Discontinuous Solutions Noel J. WalkingtonDepartment of Mathematical Sciences Carnegie Mellon University Pittsburgh, PA 15213 noelw@andrew.cmu.eduAbstract: 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