Least-squares variational principles and the finite element method: theory, formulations, and models for solid and fluid mechanics

We consider the application of least-squares variational principles and the finite element method to the numerical solution of boundary value problems arising in the fields of solid and fluid mechanics. For many of these problems least-squares principles offer many theoretical and computational adva...

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Veröffentlicht in:Finite elements in analysis and design Jg. 41; H. 7; S. 703 - 728
1. Verfasser: Pontaza, J.P.
Format: Journal Article Tagungsbericht
Sprache:Englisch
Veröffentlicht: Amsterdam Elsevier B.V 01.04.2005
Elsevier
Schlagworte:
Compressible flow
Exact sciences and technology
Fluid dynamics
Fundamental areas of phenomenology (including applications)
General theory
Incompressible flow
Least-squares finite element formulations
Physics
Plates
Shells
Solid mechanics
Static elasticity (thermoelasticity...)
Structural and continuum mechanics
Shells
Incompressible flow
Compressible flow
Plates
Least-squares finite element formulations
Compressible fluid
Fluid mechanics
Unconstrained optimization
Viscous fluid
Shear flow
Modeling
Geometrical model
Plate
Finite element method
Shell
Boundary value problem
Weak solution
Least squares method
Linear algebra
Variational calculus
Galerkin method
Incompressible fluid
Structural analysis
Viscous flow
ISSN:0168-874X, 1872-6925
Online-Zugang:Volltext
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Beschreibung
Zusammenfassung:We consider the application of least-squares variational principles and the finite element method to the numerical solution of boundary value problems arising in the fields of solid and fluid mechanics. For many of these problems least-squares principles offer many theoretical and computational advantages in the implementation of the corresponding finite element model that are not present in the traditional weak form Galerkin finite element model. For instance, the use of least-squares principles leads to a variational unconstrained minimization problem where compatibility conditions between approximation spaces never arise. Furthermore, the resulting linear algebraic problem will have a symmetric positive definite coefficient matrix, allowing the use of robust and fast iterative methods for its solution. We find that the use of high p -levels is beneficial in least-squares based finite element models and present guidelines to follow when a low p -level numerical solution is sought. Numerical examples in the context of incompressible and compressible viscous fluid flows, plate bending, and shear-deformable shells are presented to demonstrate the merits of the formulations.
Bibliographie:ObjectType-Article-2
SourceType-Scholarly Journals-1
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content type line 23
ISSN:0168-874X
1872-6925
DOI:10.1016/j.finel.2004.09.002