A residual a posteriori error estimate for the Stabilization-free Virtual Element Method
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866912858646773760 |
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| author | Berrone, Stefano Borio, Andrea Fassino, Davide Marcon, Francesca |
| author_facet | Berrone, Stefano Borio, Andrea Fassino, Davide Marcon, Francesca |
| contents | In this work, we present the a posteriori error analysis of Stabilization-Free Virtual Element Methods for the 2D Poisson equation. The abscence of a stabilizing bilinear form in the scheme allows to prove the equivalence between a suitably defined error measure and standard residual error estimators, which is not obtained in general for stabilized virtual elements. Several numerical experiments are carried out, confirming the expected behaviour of the estimator in the presence of different mesh types, and robustness with respect to jumps of the diffusion term. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_17947 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A residual a posteriori error estimate for the Stabilization-free Virtual Element Method Berrone, Stefano Borio, Andrea Fassino, Davide Marcon, Francesca Numerical Analysis 65N15, 65N22, 65N30 In this work, we present the a posteriori error analysis of Stabilization-Free Virtual Element Methods for the 2D Poisson equation. The abscence of a stabilizing bilinear form in the scheme allows to prove the equivalence between a suitably defined error measure and standard residual error estimators, which is not obtained in general for stabilized virtual elements. Several numerical experiments are carried out, confirming the expected behaviour of the estimator in the presence of different mesh types, and robustness with respect to jumps of the diffusion term. |
| title | A residual a posteriori error estimate for the Stabilization-free Virtual Element Method |
| topic | Numerical Analysis 65N15, 65N22, 65N30 |
| url | https://arxiv.org/abs/2506.17947 |