
22 Modeling shallow water ows using the DG method
2.4.2 2D Gaussian quadrature for triangular elements
The 2D quadrature rule for the canonical triangular element is given by
Equation (2.60) and the Gaussian quadrature points are listed in Table2.2
(Reddy, 1993).
∫∫
∑
ξη ξη
η
(, )
1
2
(, )
0
1
0
1
1
fd
f
iii
i
n
g
(2.60)
2.5 Approximate Riemann solvers
Since discontinuities are allowed across element boundaries, the solu-
tion for the numerical uxes can be considered as a Riemann problem.
Table2.2 Gaussian Quadrature and Weights for a Canonical Triangular Element
Number of
Gaussian
Points (n
g
) Coordinates (ξ,η) Weights (w)
Degree of
Precision (P)
1
()
ξη