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October 15, 2025Open Access

A quasi-interpolation operator yielding fully computable error bounds

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A quasi-interpolation operator demonstrates optimal error estimates in Sobolev spaces, suggesting effective finite element approximations.

Optimal estimates for both the H1 seminorm and the L2 norm errors are achieved.
The operator is defined on the entire Sobolev space without requiring additional regularity.
It operates locally within vertex patches of mesh elements, enhancing computational efficiency.
Numerical experiments confirm that the operator delivers accurate convergence rates across multiple dimensions.

Chaumont-Frelet et al. (2025) studied this question.

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October 15, 2025Open Access

View Full Paper

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Authors

A quasi-interpolation operator demonstrates optimal error estimates in Sobolev spaces, suggesting effective finite element approximations.

Optimal estimates for both the H1 seminorm and the L2 norm errors are achieved.
The operator is defined on the entire Sobolev space without requiring additional regularity.
It operates locally within vertex patches of mesh elements, enhancing computational efficiency.
Numerical experiments confirm that the operator delivers accurate convergence rates across multiple dimensions.

Chaumont-Frelet et al. (2025) studied this question.

View Full Paper

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Bookmark