, Volume 95, Supplement 1, pp 425–444 | Cite as

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

  • Lukas Korous
  • Pavel Solin


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.


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

Mathematics Subject Classification

35L65 65D99 76H05 



This research was supported by the following sources: 1. The European Regional Development Fund and the Ministry of Education, Youth and Sports of the Czech Republic under the Regional Innovation Centre for Electrical Engineering (RICE), project No. CZ.1.05/2.1.00/03.0094 2. Grant No. P105/10/1682 of the Grant Agency of the Czech Republic 3. Subcontract No. 00089911 of Battelle Energy Alliance (U.S. Department of Energy intermediary) 4. SGS (Studentska Grantova Soutez) grant number SGS-2012-039


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Copyright information

© Springer-Verlag Wien 2012

Authors and Affiliations

  1. 1.Department of Theory of Electrical Engineering, Faculty of Electrical EngineeringUniversity of West BohemiaPilsenCzech Republic
  2. 2.Department of Mathematics and StatisticsUniversity of NevadaRenoUSA
  3. 3.Institute of ThermomechanicsAcademy of Sciences of the Czech RepublicPragueCzech Republic

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