This analysis explores anisotropic approximation in Lebesgue and Besov spaces, revealing Jackson-type inequalities and implications for finite element methods.
We investigate anisotropic (piecewise) polynomial approximation of functions in Lebesgue spaces as well as anisotropic Besov spaces. For this purpose we study temporal and spacial moduli of smoothness and their properties. In particular, we prove Jackson- and Whitney-type inequalities on Lipschitz cylinders, i.e., space-time domains I× D with a finite interval I and a bounded Lipschitz domain D⊂ ᵈ, d∈. As an application, we prove a direct estimate result for adaptive space-time finite element approximation in the discontinuous setting.
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Morín et al. (2025) studied this question.
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