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High order VEM on curved domains
- Source :
- Rend. Lincei Mat. Appl., 30(3), 391-412 (2019)
- Publication Year :
- 2018
-
Abstract
- We deal with the virtual element method (VEM) for solving the Poisson equation on a domain $\Omega$ with curved boundaries. Given a polygonal approximation $\Omega_h$ of the domain $\Omega$, the standard order $m$ VEM [6], for $m$ increasing, leads to a suboptimal convergence rate. We adapt the approach of [16] to VEM and we prove that an optimal convergence rate can be achieved by using a suitable correction depending on high order normal derivatives of the discrete solution at the boundary edges of $\Omega_h$, which, to retain computability, is evaluated after applying the projector $\Pi^\nabla$ onto the space of polynomials. Numerical experiments confirm the theory.<br />Comment: 17 pages
- Subjects :
- Mathematics - Numerical Analysis
65N30, 65N99
Subjects
Details
- Database :
- arXiv
- Journal :
- Rend. Lincei Mat. Appl., 30(3), 391-412 (2019)
- Publication Type :
- Report
- Accession number :
- edsarx.1811.04755
- Document Type :
- Working Paper
- Full Text :
- https://doi.org/10.4171/RLM/853