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convergence rates 1finite element method 1fractional Hardy inequality 1Galerkin approximation 1mesh regularity 1piecewise linear elements 1

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math.NA2026

Galerkin Approximation of the Fractional Hardy Constant

Andreea Dima, Liviu I. Ignat

The paper derives sharp estimates for the discrete optimal constant in the fractional Hardy inequality and analyzes convergence rates of a Galerkin finite element method with piece…

math.NA2026

Optimal convergence rates for the finite element approximation of the Sobolev constant

Liviu I. Ignat, Enrique Zuazua

We establish optimal convergence rates for the continuous piecewise affine finite element approximation of the Sobolev constant in arbitrary dimensions N\geq 2 and for Lebesgue exp…

math.NA2026

Galerkin Approximation of the Fractional Sobolev Constant

Andreea Dima, Liviu I. Ignat

We establish sharp estimates for the discrete optimal constant of the fractional Sobolev inequality in dimension , with fractional exponent . The c…

math.NA2025

Sharp numerical approximation of the Hardy constant

Liviu I. Ignat, Enrique Zuazua

We study the finite element approximation of the best constant in the classical Hardy inequality over bounded domains containing the origin in , for .…