46 Modeling shallow water ows using the DG method
that the choice of parameters has a great inuence on the performance of
the numerical scheme.
As opposed to Equation (3.57), a mixed form given by Equation (3.56)
can be used. The boundary ux functions as given by Equation (3.65) are
used. Numerical results show that a
11
< 0 is required to achieve a stable,
convergent, and unique solution in this case. The resulting integrated
equation is given by Equation (3.68).
−−∆∆
−∆∆
−
=
−
−
++∆
++∆
−
+
−−
++
0.5 /3 /6
0.5 /6 /3
0 0.5
0 0.5
/2
/2
12
12
11 12
11 12
1
2
1
2
11
22
21 11 1
12 11 2
axx
axx
aa
aa
C
C
q
q
bC
bC
bq aC Qx
bq aC Qx
(3.68)
In the application of the discontinuous Galerkin method for elliptic
problems, the choices of the mi ...