Geometric Transformation of Finite Element Methods: Theory and Applications
by M. Holst, M. Licht
Publisher: arXiv.org 2018
Number of pages: 21
We present a new technique to apply finite element methods to partial differential equations over curved domains. Our main result is that a recently developed broken Bramble-Hilbert lemma is key in harnessing regularity in the physical problem to prove higher-order finite element convergence rates for the parametric problem.
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This book provides an excellent introduction to the elementary concepts and methods of numerical analysis for students meeting the subject for the first time. The subject matter is organized into fundamental topics and presented as a series of steps.
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