Elliptic Reconstruction and A Posteriori Error Estimates for Parabolic Variational Inequalities
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866909211569422336 |
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| author | Antil, Harbir Khandelwal, Rohit |
| author_facet | Antil, Harbir Khandelwal, Rohit |
| contents | Elliptic reconstruction property, originally introduced by Makridakis and Nochetto for linear parabolic problems, is a well-known tool to derive optimal a posteriori error estimates. No such results are known for nonlinear and nonsmooth problems such as parabolic variational inequalities (VIs). This article establishes the elliptic reconstruction property for parabolic VIs and derives a posteriori error estimates in $L^{\infty}(0,T;L^{2}(Ω))$. The estimator consists of discrete complementarity terms and standard residual. As an application, the residual-type error estimates are presented. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_17724 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Elliptic Reconstruction and A Posteriori Error Estimates for Parabolic Variational Inequalities Antil, Harbir Khandelwal, Rohit Numerical Analysis Analysis of PDEs Optimization and Control Elliptic reconstruction property, originally introduced by Makridakis and Nochetto for linear parabolic problems, is a well-known tool to derive optimal a posteriori error estimates. No such results are known for nonlinear and nonsmooth problems such as parabolic variational inequalities (VIs). This article establishes the elliptic reconstruction property for parabolic VIs and derives a posteriori error estimates in $L^{\infty}(0,T;L^{2}(Ω))$. The estimator consists of discrete complementarity terms and standard residual. As an application, the residual-type error estimates are presented. |
| title | Elliptic Reconstruction and A Posteriori Error Estimates for Parabolic Variational Inequalities |
| topic | Numerical Analysis Analysis of PDEs Optimization and Control |
| url | https://arxiv.org/abs/2402.17724 |