A performance comparison of nodal discontinuous Galerkin methods on triangles and quadrilaterals

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.

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