@Article{IJNAM-2-283,
author = {D. Xue and L. Demkowicz},
title = {Control of Geometry Induced Error in $hp$ Finite Element (FE) Simulations, I. Evaluation of FE Error for Curvilinear Geometries},
journal = {International Journal of Numerical Analysis and Modeling},
year = {2005},
volume = {2},
number = {3},
pages = {283--300},
abstract = {<p style="text-align: justify;">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.</p>},
issn = {2617-8710},
doi = {https://doi.org/},
url = {http://global-sci.org/intro/article_detail/ijnam/932.html}
}