*v(ex)*

*v(in)*

*ni*

*e*

A typical element *e *and its neighboring element along edge *i *with normal **n**i; v(in) and *v*(ex) denote

Fig. 2:

the value of a function *v *along edge *i *when approaching the edge from the interior and exterior of the

element respectively.

**3.**

**NUMERICAL MODEL**

In

this

section,

we

give

a

detailed

description

of

our

DG

sediment

transport/morphological model. To begin we define some notation. Given a spatial domain, Ω,

which has been discretized into a set of non-overlapping elements, let Ωe define the domain of a

typical element *e *and denote the boundary of the element by Γe . Our numerical approximation of

*z *will make use of piecewise smooth functions which are continuous over Ω*e *but which allow

discontinuities between elements along a given edge. We denote this space of functions by *V*h.

(in)

Given a smooth function *v *defined over *e*, we denote the values of *v *along an edge by v

when

(ex)

approaching the edge from the interior of the element and v

when approaching the edge from

the exterior of the element. The outward unit normal vector for the boundary of the element will

be denoted by **n**, and the fixed unit normal vector for a given edge *i *will be denoted by **n**i (see

Fig. 2).

In our numerical scheme, we will also make use of continuous, piecewise linear

approximations of **U **and *ζ *obtained from the ADCIRC model to compute the local sediment

transport rates.

Briefly, these approximations are obtained by solving the shallow water

10