
59Chapter four: One-dimensional conservation laws
4.4.1 Shallow water ow equations in rectangular channels
The one-dimensional computational domain (x = [0, L]) is divided into
Ne elements; let
0
12 1
xx
Ne
be a partition of the domain.
If
≤[,], 1Ix
es
e
e
e
, then a discontinuous piecewise nite element
space of polynomials m is given by Equation (4.37). Inside an element,
the unknowns are approximated by Lagrange interpolation functions as
shown in Equation (4.38). The DG formulation for an element is given by
Equation (4.39). When the explicit time integration scheme is used, the
shallow water ow equations can be solved one by one ...