content_image/403423.jpg content_image/403424.jpg
<img src='content_image/403423.jpg'>

excited by inherent numerical error. However, the figure shows data for a number of resolutions, and the trend as resolution improves is toward a flatter curve. This trend is particularly apparent in the inset which shows just the first rotational period. This behavior suggests that the code is converging to the continuum solution. 

In addition to the runs with varying resolution, Fig. 4 shows another evolution with a coarse level extending 

<img src='content_image/403424.jpg'>

twice as far but with fine levels identical to the medium resolution run just discussed. Generally, the results are the same as for the non-extended domain, indicating little effect from the boundary for the the first half-period. 

Although the fluid scheme used here is not strictly con- servative because of (i) AMR boundaries for our vertex centered scheme, (ii) our outer boundary treatment, and (iii) our use of a fluid floor, Fig. 4 shows that the frac- tional change in the volume-integrated baryon mass re- mains constant to a high degree. Similarly, the integrated angular momentum of the fluid converges to conserva- tion. 

Finally, the bottom frame of Fig. 4 shows the maxi- mum value of the constraint violation. These values in- crease with time as the numerical error accumulates, but higher resolution runs demonstrate less violation though it saturates due to the intrinsic error of the initial and boundary data. 

## Unstable, Rotating, Magnetized Star Test: 

Similarly, we evolve a rotating, magnetized star located on the unstable side. These stars, perturbed by inherent numerical error, collapse to black holes. We see no evi- dence of significant disk formation (as in e.g. [15, 16, 54– 

