2

3

1

Fig. 3:

As emphasized by Cockburn and Shu (1998), we note here that a judicious choice of

basis functions can simplify the implementation of the scheme and improve the computational

efficiency. Owing to the fact that discontinuities are permitted across element interfaces, the

choice of the basis functions are not limited by the requirement of continuity as in the CG finite

element method. Therefore, one can choose degrees of freedom that, for example, save cost in

evaluating the integrals in Eq. (15) and/or simplify the implementation of the slope limiter. In our

implementation, we use piecewise linear triangular elements described below.

Considering the "master element" as shown in Fig. 3 defined in the transformed

3

(17)

13

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