A semi-implicit discontinuous Galerkin finite element method for the numerical solution of inviscid compressible flow

Dolejší, Vít; Feistauer, Miloslav

doi:10.1016/j.jcp.2004.01.023

Cited by 102 publications

(68 citation statements)

References 27 publications

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“…In the last decades the discontinuous Galerkin (DG) method has been used extensively for approximation of partial differential equations, see, e.g., [9,11,13,20,36,40] and the references therein. The method is popular due to its flexibility: it is based on the Galerkin, i.e.…”

Section: Discontinuous Galerkin Methods and The Multidimensional Eg Opmentioning

confidence: 99%

Adaptive discontinuous evolution Galerkin method for dry atmospheric flow

Yelash

Müller

Lukáčová-Medviďová

et al. 2014

Journal of Computational Physics

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Section: Discontinuous Galerkin Methods and The Multidimensional Eg Opmentioning

confidence: 99%

Adaptive discontinuous evolution Galerkin method for dry atmospheric flow

Yelash

Müller

Lukáčová-Medviďová

et al. 2014

Journal of Computational Physics

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“…Nearly simultaneously the DGFE techniques were developed for the numerical solution of second-order elliptic problems or parabolic problems [2,57] and a biharmonic problem [6]. Further, the DGFE method was applied to transport-reaction problems [13], nonlinear conservation laws [17,40], convection-diffusion linear or nonlinear problems [11,18,19,35,33], compressible flow [8][9][10]21,23,36,56], simulation of compressible low Mach number flows at incompressible limit [25,34], solution of incompressible viscous flow [52,55], porous media flow [53], shallow water flow [20], the HamiltonJacobi equations [38], the Schrödinger equation [42] and the Maxwell equations [37]. Theoretical analysis of various types of the DGFE method applied to elliptic problems can be found, e.g.…”

Section: Introductionmentioning

confidence: 99%

Analysis of space–time discontinuous Galerkin method for nonlinear convection–diffusion problems

et al. 2010

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The paper presents the theory of the discontinuous Galerkin finite element method for the space-time discretization of a nonstationary convection-diffusion initial-boundary value problem with nonlinear convection and linear diffusion. The problem is not singularly perturbed with dominating convection. The discontinuous Galerkin method is applied separately in space and time using, in general, different space grids on different time levels and different polynomial degrees p and q in space and time dicretization. In the space discretization the nonsymmetric, symmetric and incomplete interior and boundary penalty (NIPG, SIPG, IIPG) approximation of diffusion terms is used. The paper is concerned with the proof of error estimates in "L 2 (L 2 )"-and "DG"-norm formed by the "L 2 (H 1 )"-seminorm and penalty terms. A special technique based on the use of the Gauss-Radau interpolation and numerical integration has been used for the derivation of an abstract error estimate. In the "DG"-norm the error estimates are optimal with respect to the size of the space grid.

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“…Let us mention in particular the solution of nonlinear conservation laws ( [11], [29], [19]) and compressible flow ( [5], [6], [7], [13], [15], [17], [24], [26], [48]). A survey of DGFE methods, techniques and some applications can be found in [9] and [10].…”

Section: Introductionmentioning

confidence: 99%

“…Therefore, it is suitable to apply implicit or semiimplicit methods. In [38] implicit θ-schemes are analyzed, [16] is concerned with the analysis of a semi-implicit linearized scheme for a nonlinear convection-diffusion problem and in [15] an efficient semi-implicit method for the solution of compressible Euler equations was developed. However, these methods have low order of accuracy in time.…”

Section: Introductionmentioning

confidence: 99%