A posteriori error analysis of the virtual element method for second-order quasilinear elliptic PDEs
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866914957992394752 |
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| author | Congreve, Scott Hodson, Alice |
| author_facet | Congreve, Scott Hodson, Alice |
| contents | In this paper we develop a $C^0$-conforming virtual element method (VEM) for a class of second-order quasilinear elliptic PDEs in two dimensions. We present a posteriori error analysis for this problem and derive a residual based error estimator. The estimator is fully computable and we prove upper and lower bounds of the error estimator which are explicit in the local mesh size. We use the estimator to drive an adaptive mesh refinement algorithm. A handful of numerical test problems are carried out to study the performance of the proposed error indicator. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_17779 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A posteriori error analysis of the virtual element method for second-order quasilinear elliptic PDEs Congreve, Scott Hodson, Alice Numerical Analysis 65N50, 65N30 In this paper we develop a $C^0$-conforming virtual element method (VEM) for a class of second-order quasilinear elliptic PDEs in two dimensions. We present a posteriori error analysis for this problem and derive a residual based error estimator. The estimator is fully computable and we prove upper and lower bounds of the error estimator which are explicit in the local mesh size. We use the estimator to drive an adaptive mesh refinement algorithm. A handful of numerical test problems are carried out to study the performance of the proposed error indicator. |
| title | A posteriori error analysis of the virtual element method for second-order quasilinear elliptic PDEs |
| topic | Numerical Analysis 65N50, 65N30 |
| url | https://arxiv.org/abs/2409.17779 |