An adaptive \(hp\)-DG method with dynamically-changing meshes for non-stationary compressible Euler equations
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 236:49094924, 2012; Schnepp and Weiland, Radio Science, vol46, 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.
euler equations \(hp\)-adaptivity numerical simulation finite element method discontinuous galerkin method automatic adaptivity dynamically changing meshes 35l65 65d99 76h05