Adaptive Discontinuous Galerkin Methods with Applications

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Many problems of engineering interest are posed in complex, possibly non-smooth and three-dimensional domains. They often involve multiple physical models and scales, as well as highly varying or non-linear material properties. Advanced numerical techniques are required for meaningful predictions. To achieve improved and high-order accurate simulation outputs, we shall focus on the development and implementation of discontinuous Galerkin (DG) finite element methods, combined with adaptive refinement strategies. In recent years, these methods established themselves as robust and flexible simulation techniques for wide classes of problems in computational fluid dynamics, structural mechanics and electro-magnetics. They are naturally suited for adaptive computations, and for providing a unified computational platform for simulating coupled multi-physics models in three space dimensions.