Adaptive Discontinuous Galerkin Methods with Applications

许多工程上感兴趣的问题都是在复杂的、可能是非光滑的和三维域中提出的。它们通常涉及多个物理模型和比例，以及高度变化或非线性的材料属性。需要先进的数值技术才能做出有意义的预测。为了获得更好的和高精度的模拟输出，我们将重点开发和实施间断伽辽金(DG)有限元方法，并结合自适应细化策略。近年来，这些方法成为计算流体力学、结构力学和电磁学中各种问题的稳健和灵活的模拟技术。它们自然适合于自适应计算，并为模拟三维空间中的耦合多物理模型提供了一个统一的计算平台。

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.