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Advanced Numerical Methods in the Mathematical Sciences

Tan Bui-Thanh, University of Texas at Austin
Some Recent Advances in Hybridized Discontinuous Galerkin Methods


We will present several new developments on the emerging Hybridized Discontinuous Galerkin (HDG) method. First, starting either from the Godunov upwind idea or from the Rankine-Hugoniot condition we derive a unified HDG framework for linear PDEs that allows one to uncover new HDG methods and recover most of the existing ones for a large class of PDE including the Friedrichs' systems. Analysis and numerical results for the unified framework will be presented. Second, we will present an IMEX scheme for the HDG method with application to atmospheric sciences. Third, we will present a multilevel HDG solver that is promising to be one of the fast and parallel solvers for large-scale problem. Fourth, we will present our work on parallel \(hp\) method for HDG methods. Finally, a non-conforming HDG will be introduced and analyzed.