An adaptive hp-DG method with dynamically-changing meshes for non-stationary compressible Euler equations

作者：Korous Lukas^*; Solin Pavel

来源：Computing, 2013, 95(1): S425-S444.

DOI：10.1007/s00607-012-0257-1

• Numerical simulation
• Finite element method
• Euler equations
• hp-adaptivity
• Discontinuous Galerkin method
• Automatic adaptivity
• Dynamically changing meshes

Compressible Euler equations describing the motion of compressible inviscid fluids are typically solved by means of low-order finite volume (FVM) or finite element (FEM) methods. A promising recent alternative to these low-order methods is the higher-order discontinuous Galerkin (hp-DG) method (Schnepp and Weiland, J Comput Appl Math 236: 4909-4924, 2012; Schnepp and Weiland, Radio Science, vol 46, RS0E03, 2011) that combines the stability of FVM with excellent approximation properties of higher-order FEM. This paper presents a novel hp-adaptive algorithm for the hp-DG method which is based on meshes that change dynamically in time. The algorithm reduces the order of the approximation on shocks and keeps higher-order elements where the approximation is smooth, which leads to an efficient discretization of the time-dependent problem. The method is described and numerical examples are presented.

• 出版日期2013-5