Convergence and error estimates for pseudo-polyharmonic div-curl and elastic interpolation on a bounded domain - Archive ouverte HAL Access content directly
Journal Articles Journal of Numerical Analysis and Approximation Theory Year : 2023

Convergence and error estimates for pseudo-polyharmonic div-curl and elastic interpolation on a bounded domain

Mohammed-Najib Benbourhim
Pedro Gonzalez-Casanova

Abstract

This paper establishes convergence rates and error estimates for the pseudo-polyharmonic div-curl and elastic interpolation. This type of interpolation is based on a combination of the divergence and the curl of a multivariate vector field and minimizing an appropriate functional energy related to the divergence and curl. Convergence rates and error estimates are established when the interpolated vector field is assumed to be in the classical fractional vectorial Sobolev space on an open bounded set with a Lipschitz-continuous boundary. The error estimates introduced in this work are sharp and the rate of convergence depends algebraically on the fill distance of the scattered data nodes. More precisely, the order of convergence depends, essentially, on the smoothness of the target vector field, on the dimension of the Euclidean space and on the null space of corresponding Sobolev semi-norm.

Dates and versions

hal-04358836 , version 1 (21-12-2023)

Identifiers

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Mohammed-Najib Benbourhim, Abderrahman Bouhamidi, Pedro Gonzalez-Casanova. Convergence and error estimates for pseudo-polyharmonic div-curl and elastic interpolation on a bounded domain. Journal of Numerical Analysis and Approximation Theory, 2023, 52 (1), pp.34-56. ⟨10.33993/jnaat521-1306⟩. ⟨hal-04358836⟩
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