Piecewise polynomial approximation on non-Lipschitz domains

2025/11/27 by Hewett, D P
#41A10 #41A25 #65N30 #65N38 #FOS: Mathematics #Numerical Analysis (math.NA)

paper · doi:10.48550/arxiv.2511.22628

Abstract

We prove best approximation error estimates for discontinuous piecewise polynomial approximation in fractional Sobolev spaces on non-Lipschitz meshes of non-Lipschitz domains. In particular, the boundary of the domain, and the boundaries of the mesh elements, can be fractal.

Citations

• Properties of IFS attractors with non-empty interiors, related rough domains, and associated function spaces and scattering problems
• Integral equation methods for acoustic scattering by fractals
• Numerical evaluation of singular integrals on non-disjoint self-similar fractal sets
• hp-Version discontinuous Galerkin methods on essentially arbitrarily-shaped elements
• The Finite Element Method for Elliptic Problems

Related

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• Lower Bounds of the Discretization for Piecewise Polynomials
• Approximation by C¹ Splines on Piecewise Conic Domains