High-order adaptive methods for hyperbolic conservation laws

这一建议旨在发展新的高阶自适应算法，用于双曲型守恒律数值解的间断Galerkin方法(DGM)。这些方法对于由偏微分方程组模拟的大规模问题的解的计算变得越来越重要。它们吸引人的特点是单元守恒性、高精度、易适应性和简单的并行求解过程。它们被广泛应用于流体动力学、空气声学、电磁学和光学等领域。这项工作将导致更准确的计算机模拟和更短的设计时间。

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.