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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 .…
math.NA2025
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…