Feistauer, Miloslav, Dolejší, Vít
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This paper is concerned with the application of the discontinuous Galerkin finite element method to the numerical solution of the compressible Navier-Stokes equations. The attention is paid to the derivation of discontinuous Galerkin finite element schemes and to the investigation of the accuracy of the symmetric as well as nonsymmetric discretization.
Kučera, Václav
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This work is concerned with the introduction of a new numerical scheme based on the discontinuous Galerkin (DG) method. We propose to follow the methodology of higher order finite volume schemes and introduce a reconstruction operator into the DG scheme. This operator constructs higher order piecewise polynomial reconstructions from the lower order DG scheme. Such a procedure was proposed already in [2] based on heuristic arguments, however we provide a rigorous derivation, which justifies...
Raphaèle Herbin, Walid Kheriji, Jean-Claude Latche (2012)
ESAIM: Proceedings
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We review in this paper a class of schemes for the numerical simulation of compressible flows. In order to ensure the stability of the discretizations in a wide range of Mach numbers and introduce sufficient decoupling for the numerical resolution, we choose to implement and study pressure correction schemes on staggered meshes. The implicit version of the schemes is also considered for the theoretical study. We give both algorithms for the barotropic Navier-Stokes equations, for the...
Hozman, Jiří
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This paper is devoted to barrier options and the main objective is to develop a sufficiently robust, accurate and efficient method for computation of their values driven according to the well-known Black-Scholes equation. The main idea is based on the discontinuous Galerkin method together with a spatial adaptive approach. This combination seems to be a promising technique for the solving of such problems with discontinuous solutions as well as for consequent optimization of the number...