Lowest order stabilization free Virtual Element Method for the 2D Poisson equation
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2021
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| _version_ | 1866908942822539264 |
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| author | Berrone, Stefano Borio, Andrea Marcon, Francesca |
| author_facet | Berrone, Stefano Borio, Andrea Marcon, Francesca |
| contents | We introduce and analyse the first order Enlarged Enhancement Virtual Element Method (E$^2$VEM) for the Poisson problem. The method allows the definition of bilinear forms that do not require a stabilization term, thanks to the exploitation of higher order polynomial projections that are made computable by suitably enlarging the enhancement (from which comes the prefix of the name E$^2$) property of local virtual spaces. The polynomial degree of local projections is chosen based on the number of vertices of each polygon. We provide a proof of well-posedness and optimal order a priori error estimates. Numerical tests on convex and non-convex polygonal meshes confirm the criterium for well-posedness and the theoretical convergence rates. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2103_16896 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Lowest order stabilization free Virtual Element Method for the 2D Poisson equation Berrone, Stefano Borio, Andrea Marcon, Francesca Numerical Analysis 65N12, 65N15, 65N30 We introduce and analyse the first order Enlarged Enhancement Virtual Element Method (E$^2$VEM) for the Poisson problem. The method allows the definition of bilinear forms that do not require a stabilization term, thanks to the exploitation of higher order polynomial projections that are made computable by suitably enlarging the enhancement (from which comes the prefix of the name E$^2$) property of local virtual spaces. The polynomial degree of local projections is chosen based on the number of vertices of each polygon. We provide a proof of well-posedness and optimal order a priori error estimates. Numerical tests on convex and non-convex polygonal meshes confirm the criterium for well-posedness and the theoretical convergence rates. |
| title | Lowest order stabilization free Virtual Element Method for the 2D Poisson equation |
| topic | Numerical Analysis 65N12, 65N15, 65N30 |
| url | https://arxiv.org/abs/2103.16896 |