Year: 2004
Author: Pavel Bochev
International Journal of Numerical Analysis and Modeling, Vol. 1 (2004), Iss. 1 : pp. 49–64
Abstract
Least-squares principles use artificial "energy" functionals to provide a Rayleigh-Ritz-like setting for the finite element method. These functionals are defined in terms of PDE’s residuals and are not unique. We show that viable methods result from reconciliation of a mathematical setting dictated by the norm-equivalence of least-squares functionals with practicality constraints dictated by the algorithmic design. We identify four universal patterns that arise in this process and develop this paradigm for first-order ADN elliptic systems. Special attention is paid to the effects that each discretization pattern has on the computational and analytic properties of finite element methods, including error estimates, conditioning of the algebraic systems and the existence of efficient preconditioners.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2004-IJNAM-965
International Journal of Numerical Analysis and Modeling, Vol. 1 (2004), Iss. 1 : pp. 49–64
Published online: 2004-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 16
Keywords: finite elements least-squares first-order elliptic systems.