Control of Geometry Induced Error in $hp$ Finite Element (FE) Simulations, I. Evaluation of FE Error for Curvilinear Geometries
Year: 2005
International Journal of Numerical Analysis and Modeling, Vol. 2 (2005), Iss. 3 : pp. 283–300
Abstract
The paper discusses a general framework for handling curvilinear geometries in high accuracy Finite Element (FE) simulations, for both elliptic and Maxwell problems. Based on the differential manifold concept, the domain is represented as a union of geometrical blocks prescribed with globally compatible, explicit or implicit parameterizations. The idea of parametric $H^1$-, $H(curl)$- and $H(div)$-conforming elements is reviewed, and the concepts of exact geometry elements and isoparametric elements are discussed. The paper focuses then on isoparametric elements, and two ways of computing FE discretization errors: a popular one, neglecting the geometry approximation, and a precise one, utilizing the exact geometry representation. Presented numerical examples indicate the necessity of accounting for the geometry error in FE error calculations, especially for the $H(curl)$ problems.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2005-IJNAM-932
International Journal of Numerical Analysis and Modeling, Vol. 2 (2005), Iss. 3 : pp. 283–300
Published online: 2005-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 18
Keywords: geometry approximation curvilinear $hp$ Finite Element(FE) meshes error evaluation Exact Geometry Integration (EGI).