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Utility of a finite element solution algorithm for initial-value problemsThe Galerkin criterion within a finite element Weighted Residuals formulation is employed to establish an implicit solution algorithm for an initial-value partial differential equation. Numerical solutions of a transient parabolic and a hyperbolic equation, obtained using linear, quadratic and two cubic finite element basis functions, are employed to quantize accuracy and confirm and refine theoretical convergence rate estimates. The linear basis algorithm for the hyperbolic equation displays excellent accuracy on a coarse computational grid and a high-order convergence rate with discretization refinement. Good accuracy and a strong convergence rate in surface flux are determined for a nonhomogeneous Neumann boundary constraint applied to a parabolic equation. The results amply demonstrate the impact of the nondiagonal finite element initial-value matrix structure on solution accuracy and/or convergence rate.
Document ID
19790069104
Acquisition Source
Legacy CDMS
Document Type
Reprint (Version printed in journal)
Authors
Baker, A. J.
(Tennessee, University Knoxville, Tenn., United States)
Soliman, M. O.
(Tennessee Univ. Knoxville, TN, United States)
Date Acquired
August 9, 2013
Publication Date
September 1, 1979
Publication Information
Publication: Journal of Computational Physics
Volume: 32
Subject Category
Numerical Analysis
Accession Number
79A53117
Funding Number(s)
CONTRACT_GRANT: NSG-1261
Distribution Limits
Public
Copyright
Other

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