High-order adaptive methods for hyperbolic conservation laws

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This proposal is aimed at the development of new high-order adaptive algorithms for the numerical solution of hyperbolic conservation laws using discontinuous Galerkin methods (DGM). These methods are becoming important for the computation of solutions of large scale problems modeled by partial differential equations. Their attractive features are an element-wise conservation property, high-order accuracy, easy adaptivity, and simple parallel solution procedures. They are used in such diverse applications as fluid dynamics, aeroacoustics, electromagnetics, and optics. This work will lead to more accurate computer simulations and shorter design times.