Comparison of high-order finite volume and discontinuous Galerkin methods on 3D unstructured grids

A.F. Antoniadis, K.H. Iqbal, E. Shapiro, N. Asproulis, D. Drikakis

Research output: Contribution to conferencePaper

Abstract

The paper presents a direct comparison of convergence properties of finite volume and discontinuous Galerkin methods of the same nominal order of accuracy. Convergence is evaluated on tetrahedral grids for an advection equation and manufactured solution of Euler equations. It is shown that for the test cases considered, the discontinuous Galerkin discretisation tends to recover the asymptotic range of convergence on coarser grids and yields a lower error norm by comparison with the finite volume discretisation.

Conference

ConferenceInternational Conference on Numerical Analysis and Applied Mathematics: Numerical Analysis and Applied Mathematics, ICNAAM 2011
Abbreviated titleICNAAM 2011
CountryGreece
CityHalkidiki
Period19/09/1125/09/11

Fingerprint

Unstructured Grid
Discontinuous Galerkin Method
Finite Volume
Discretization
Higher Order
Grid
Advection Equation
Discontinuous Galerkin
Euler Equations
Convergence Properties
Categorical or nominal
Tend
Norm
Range of data

Keywords

  • Galerkin methods
  • numerical modeling
  • numerical solutions
  • finite volume method
  • high-order

Cite this

Antoniadis, A. F., Iqbal, K. H., Shapiro, E., Asproulis, N., & Drikakis, D. (2011). Comparison of high-order finite volume and discontinuous Galerkin methods on 3D unstructured grids. 1886-1889. Paper presented at International Conference on Numerical Analysis and Applied Mathematics: Numerical Analysis and Applied Mathematics, ICNAAM 2011, Halkidiki, Greece. https://doi.org/10.1063/1.3636979
Antoniadis, A.F. ; Iqbal, K.H. ; Shapiro, E. ; Asproulis, N. ; Drikakis, D. / Comparison of high-order finite volume and discontinuous Galerkin methods on 3D unstructured grids. Paper presented at International Conference on Numerical Analysis and Applied Mathematics: Numerical Analysis and Applied Mathematics, ICNAAM 2011, Halkidiki, Greece.4 p.
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Antoniadis, AF, Iqbal, KH, Shapiro, E, Asproulis, N & Drikakis, D 2011, 'Comparison of high-order finite volume and discontinuous Galerkin methods on 3D unstructured grids' Paper presented at International Conference on Numerical Analysis and Applied Mathematics: Numerical Analysis and Applied Mathematics, ICNAAM 2011, Halkidiki, Greece, 19/09/11 - 25/09/11, pp. 1886-1889. https://doi.org/10.1063/1.3636979

Comparison of high-order finite volume and discontinuous Galerkin methods on 3D unstructured grids. / Antoniadis, A.F.; Iqbal, K.H.; Shapiro, E.; Asproulis, N.; Drikakis, D.

2011. 1886-1889 Paper presented at International Conference on Numerical Analysis and Applied Mathematics: Numerical Analysis and Applied Mathematics, ICNAAM 2011, Halkidiki, Greece.

Research output: Contribution to conferencePaper

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AU - Iqbal, K.H.

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AU - Asproulis, N.

AU - Drikakis, D.

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N2 - The paper presents a direct comparison of convergence properties of finite volume and discontinuous Galerkin methods of the same nominal order of accuracy. Convergence is evaluated on tetrahedral grids for an advection equation and manufactured solution of Euler equations. It is shown that for the test cases considered, the discontinuous Galerkin discretisation tends to recover the asymptotic range of convergence on coarser grids and yields a lower error norm by comparison with the finite volume discretisation.

AB - The paper presents a direct comparison of convergence properties of finite volume and discontinuous Galerkin methods of the same nominal order of accuracy. Convergence is evaluated on tetrahedral grids for an advection equation and manufactured solution of Euler equations. It is shown that for the test cases considered, the discontinuous Galerkin discretisation tends to recover the asymptotic range of convergence on coarser grids and yields a lower error norm by comparison with the finite volume discretisation.

KW - Galerkin methods

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KW - numerical solutions

KW - finite volume method

KW - high-order

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Antoniadis AF, Iqbal KH, Shapiro E, Asproulis N, Drikakis D. Comparison of high-order finite volume and discontinuous Galerkin methods on 3D unstructured grids. 2011. Paper presented at International Conference on Numerical Analysis and Applied Mathematics: Numerical Analysis and Applied Mathematics, ICNAAM 2011, Halkidiki, Greece. https://doi.org/10.1063/1.3636979