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2011•AIP conference proceedingsRequires access

Comparison of High-order Finite Volume and Discontinuous Galerkin Methods on 3D Unstructured Grids

Antonis F. Antoniadis, Kamran Iqbal, Evgeniy Shapiro, Nikolaos Asproulis, Dimitris Drikakis, Theodore E. Simos, George Psihoyios, Ch. Tsitouras, Zacharias A. Anastassi

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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.

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What this paper is about

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.

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Available 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.

Key concepts: Discontinuous Galerkin method, Finite volume method, Discretization, Mathematics, Backward Euler method, Euler equations, Applied mathematics, Rate of convergence

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