Discontinuous galerkin methods for flow and electro-magnetic problems

不连续伽辽金方法是用于科学和工程中复杂现象的计算机模拟的专门数值方法。虽然第一个不连续伽辽金方法是在1973年发明的，但这些方法在90年代经历了重大发展，使它们成为计算流体动力学的主流。近年来，这些方法被应用于许多其他的工程问题，包括电磁学和结构力学。近年来不连续伽辽金方法的成功可归功于其灵活性和通用性。这些方法可以鲁棒地处理几乎任何类型的偏微分方程，以及在计算域内类型变化的方程。它们非常适合于多物理场应用和复杂几何形状中具有高度变化的材料特性的问题。不连续伽辽金方法可以方便地处理不规则细化网格和可变逼近度；一种被称为hp自适应的特性。

Discontinuous Galerkin methods are specialized numerical methods for the computer simulation of complex phenomena in the sciences and engineering. Although the first discontinuous Galerkin method was devised back in 1973, these methods experienced a significant development during the nineties which brought them to the mainstream of computational fluid dynamics. In recent years, these methods are being applied to many other problems of engineering interest including electro-magnetics and structural mechanics. The recent success of discontinuous Galerkin methods can be attributed to their flexibility and versatility. These methods can deal robustly with partial differential equations of almost any kind, as well as with equations whose type changes within the computational domain. They are ideally suited for multi-physics applications and for problems with highly varying material properties in complex geometries. Moreover, discontinuous Galerkin methods can easily handle irregularly refined meshes and variable approximation degrees; a property referred to as hp-adaptivity.