Journal
CLASSICAL AND QUANTUM GRAVITY
Volume 23, Issue 16, Pages S421-S445Publisher
IOP PUBLISHING LTD
DOI: 10.1088/0264-9381/23/16/S08
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Efforts to achieve better accuracy in numerical relativity have so far focused either on implementing second-order accurate adaptive mesh refinement or on defining higher order accurate differences and update schemes. Here, we argue for the combination, that is a higher order accurate adaptive scheme. This combines the power that adaptive gridding techniques provide to resolve fine scales ( in addition to a more efficient use of resources) together with the higher accuracy furnished by higher order schemes when the solution is adequately resolved. To define a convenient higher order adaptive mesh refinement scheme, we discuss a few different modifications of the standard, second-order accurate approach of Berger and Oliger. Applying each of these methods to a simplemodel problem, we find these options have unstablemodes. However, a novel approach to dealing with the grid boundaries introduced by the adaptivity appears stable and quite promising for the use of high order operators within an adaptive framework.
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