Obtaining higher-order Galerkin accuracy when the boundary is polygonally approximated
Abstract: Inspired by the methods developed in J. H. Bramble, T. Dupont, and V. Thomée (“Projection methods for Dirichlet’s problem in approximating polygonal domains with boundary-value corrections,” Math. Comput., vol. 26, no. 120, pp. 869–879, 1972), we introduce a new technique that yields a symmetric formulation and has similar performance. The new method is based on a Robin-type problem on an approximate polygonal domain. Optimal error estimates in the energy norm are proved for piecewise quadratics and cubics. We provide numerical experiments that show our theoretical results are sharp.
- Location
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Deutsche Nationalbibliothek Frankfurt am Main
- Extent
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Online-Ressource
- Language
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Englisch
- Bibliographic citation
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Obtaining higher-order Galerkin accuracy when the boundary is polygonally approximated ; volume:33 ; number:1 ; year:2025 ; pages:55-86 ; extent:32
Journal of numerical mathematics ; 33, Heft 1 (2025), 55-86 (gesamt 32)
- Creator
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Dupont, Todd
Guzmán, Johnny
Scott, L. Ridgway
- DOI
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10.1515/jnma-2023-0135
- URN
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urn:nbn:de:101:1-2503010514211.948253435584
- Rights
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Open Access; Der Zugriff auf das Objekt ist unbeschränkt möglich.
- Last update
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15.08.2025, 7:36 AM CEST
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Associated
- Dupont, Todd
- Guzmán, Johnny
- Scott, L. Ridgway
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