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A performance comparison of nodal discontinuous Galerkin methods on triangles and quadrilaterals
Author(s) -
Wirasaet D.,
Tanaka S.,
Kubatko E. J.,
Westerink J. J.,
Dawson C.
Publication year - 2010
Publication title -
international journal for numerical methods in fluids
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.938
H-Index - 112
eISSN - 1097-0363
pISSN - 0271-2091
DOI - 10.1002/fld.2376
Subject(s) - quadrilateral , mathematics , basis function , basis (linear algebra) , finite element method , legendre polynomials , galerkin method , geometry , mathematical analysis , structural engineering , engineering
Abstract This work presents a study on the performance of nodal bases on triangles and on quadrilaterals for discontinuous Galerkin solutions of hyperbolic conservation laws. A nodal basis on triangles and two tensor product nodal bases on quadrilaterals are considered. The quadrilateral element bases are constructed from the Lagrange interpolating polynomials associated with the Legendre–Gauss–Lobatto points and from those associated with the classical Legendre–Gauss points. Settings of interest concern the situation in which a mesh of triangular elements is obtained by dividing each quadrilateral element into two triangular elements or vice versa , the mesh of quadrilateral elements is obtained by merging two adjacent triangular elements. To assess performance, we use a linear advecting rotating plume transport problem as a test case. For cases where the order of the basis is low to moderate, the computing time used to reach a given final time for the quadrilateral elements is shorter than that for the triangular elements. The numerical results also show that the quadrilateral elements yield higher computational efficiency in terms of cost to achieve similar accuracy. Copyright © 2010 John Wiley & Sons, Ltd.