Anisotropic approximation on space-time domains

2025/06/24 by Pedro Morín, Morin, Pedro, Cornelia Schneider +2
Computer Science · Earth and Planetary Sciences · Engineering · #Advanced Mathematical Modeling in Engineering #FOS: Mathematics #Geophysics and Gravity Measurements #Heat Transfer and Mathematical Modeling #Numerical Analysis (math.NA)

paper · pdf · doi:10.48550/arxiv.2506.19517

openalex publication_date 2025/06/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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⊂ \R^d, d∈ \N. As an application, we prove a direct estimate result for adaptive space-time finite element approximation in the discontinuous setting.

Citations

• Adaptive Mesh Refinement for arbitrary initial Triangulations
• Anisotropic Besov regularity of parabolic PDEs
• Approximation classes for adaptive time-stepping finite element methods

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• Piecewise polynomial approximation on non-Lipschitz domains
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