
36 Modeling shallow water ows using the DG method
===
===
−
−
(2)2
(3)
1
uux
uu
(3.25)
−−
−
−−
=−
1/22/3 1/6
2/302/3
1/62/3 1/2
13/6
2/3
1/6
1
2
3
u
u
u
(3.26)
=
2
2.5
3
1
2
3
u
u
u
(3.27)
3.2 1D Linear convection
In this section, the discontinuous Galerkin method is applied to model
the one-dimensional linear convection problem as given by Equation
(3.28). The one-dimensional domain is x ∈ [0, 1], and is divided into Ne
linear elements with Ne + 1 nodes
+
12 1
xx x
Ne
. For demon-
stration purpose, only linear and uniform size elements are used in this
example (Figure3.3). However, the element ...