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Adaptive schemes generally aim at reducing CPU cost by adjusting the quality of the representation to capture essential features of the solution. In this chapter, we explore four different strategies for performing such refinement. The following developments are motivated in part by the experiences with MW representations outlined in the previous chapter. In particular, these indicated that while “refinement” can be naturally implemented in conjunction with wavelet representation, for instance by increasing the levels of details, a uniform or brute-force refinement is likely to require excessive CPU resources, even for simple examples. Adaptive schemes consequently strive to perform such refinements locally where needed, in an effort to minimize necessary computational resources.
KeywordsDual Problem Posteriori Error Burger Equation Adaptive Method Approximation Space
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