Supremum norm A Posteriori Error control of Quadratic Finite Element Method for the Signorini problem
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866911747601858560 |
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| author | Khandelwal, Rohit Porwal, Kamana Wadhawan, Tanvi |
| author_facet | Khandelwal, Rohit Porwal, Kamana Wadhawan, Tanvi |
| contents | In this paper, we develop a new residual-based pointwise a posteriori error estimator of the quadratic finite element method for the Signorini problem. The supremum norm a posteriori error estimates enable us to locate the singularities locally to control the pointwise errors. In the analysis the discrete counterpart of contact force density is constructed suitably to exhibit the desired sign property. We employ a priori estimates for the standard Green's matrix for the divergence type operator and introduce the upper and lower barriers functions by appropriately modifying the discrete solution. Finally, we present numerical experiments that illustrate the excellent performance of the proposed error estimator. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_02181 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Supremum norm A Posteriori Error control of Quadratic Finite Element Method for the Signorini problem Khandelwal, Rohit Porwal, Kamana Wadhawan, Tanvi Numerical Analysis In this paper, we develop a new residual-based pointwise a posteriori error estimator of the quadratic finite element method for the Signorini problem. The supremum norm a posteriori error estimates enable us to locate the singularities locally to control the pointwise errors. In the analysis the discrete counterpart of contact force density is constructed suitably to exhibit the desired sign property. We employ a priori estimates for the standard Green's matrix for the divergence type operator and introduce the upper and lower barriers functions by appropriately modifying the discrete solution. Finally, we present numerical experiments that illustrate the excellent performance of the proposed error estimator. |
| title | Supremum norm A Posteriori Error control of Quadratic Finite Element Method for the Signorini problem |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2401.02181 |