An Investigation Of The Method Of Finite Elements With Accuracy Comparisons To The Method Of Finite Differences For Solution Of The Transient Heat Conduction Equation Using Optimum Implicit Formulations
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An Investigation Of The Method Of Finite Elements With Accuracy Comparisons To The Method Of Finite Differences For Solution Of The Transient Heat Conduction Equation Using Optimum Implicit Formulations
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Author : Joseph C. Geneczko
language : en
Publisher:
Release Date : 1978
An Investigation Of The Method Of Finite Elements With Accuracy Comparisons To The Method Of Finite Differences For Solution Of The Transient Heat Conduction Equation Using Optimum Implicit Formulations written by Joseph C. Geneczko and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1978 with categories.
The one-dimensional transient heat conduction equation, with Dirichlet boundary conditions, is solved by the method of finite-elements, employing a quadratic interpolation function. The numerical solutions are investigated with respect to accuracy and stability, and compared to like results attained by the method of finite-differences, and the finite-element method with linear interpolation. The version of the finite-element method used was based on a variational principle which is stationary in time; the temporal behavior of the differential equation is treated with a finite-difference approximation. This method is equivalent to the method of Galerkin, called the Method of Weighted Residuals. The inherent discontinuity between the initial condition and boundary conditions was accounted for by substituting the exact analytical solution at the first time step and numerically computating from there. An equivalency relationship between the two finite-element methods is shown to exist. The finite-difference version of the Crank-Nicolson method is found to be more accurate than the finite-element version; for the fully implicit method, the opposite is found to be true. In the optimum implicit method, both finite-element solutions are shown equivalent to the finite-difference solution for a Fourier modulus of one. For other values of this parameter, the finite-element solution is more accurate. (Author).
An Investigation Of The Method Of Finite Elements With Accuracy Comparisons To The Method Of Finite Differences For Solution Of The Transient Heat Conduction Equation Using Optimum Implicit Formulations
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Author : Joseph C. Geneczko (CAPT, USAF.)
language : en
Publisher:
Release Date : 1978
An Investigation Of The Method Of Finite Elements With Accuracy Comparisons To The Method Of Finite Differences For Solution Of The Transient Heat Conduction Equation Using Optimum Implicit Formulations written by Joseph C. Geneczko (CAPT, USAF.) and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1978 with Boundary value problems categories.
An Investigation Of The Numerical Methods Of Finite Differences And Finite Elements For Digital Computer Solution Of The Transient Heat Conduction Diffusion Equation Using Optimum Implicit Formulations
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Author : Charles R. Martin
language : en
Publisher:
Release Date : 1978
An Investigation Of The Numerical Methods Of Finite Differences And Finite Elements For Digital Computer Solution Of The Transient Heat Conduction Diffusion Equation Using Optimum Implicit Formulations written by Charles R. Martin and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1978 with categories.
The transient heat conduction equation, with Dirichlet and Neumann boundary conditions, is solved by the methods of finite-differences and finite-elements, and the numerical solutions are investigated with respect to accuracy and stability. A general six point finite-difference expression is used for which there exists a high order accurate modification. The finite-element method used is based on a stationary variational principle. Several methods for treating accuracy and convergence problems which result from a discontinuity in the initial condition are investigated. The Crank-Nicolson method is a special case of both the finite-difference and finite-element methods. The finite-difference version of the Crank-Nicolson method is shown to be more accurate than the finite-element version, especially when a discontinuity exists between the initial condition and the boundary conditions. The high order accurate schemes for both finite-differences and finite-elements are shown to be equivalent for the case of linear elements. Some of the results suggest the possibility of finding a finite-element scheme which is highly accurate in a mean square sensr over the entire solution domain. (Author).
Scientific And Technical Aerospace Reports
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Author :
language : en
Publisher:
Release Date : 1986
Scientific And Technical Aerospace Reports written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1986 with Aeronautics categories.
Technical Abstract Bulletin
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Author :
language : en
Publisher:
Release Date : 1979
Technical Abstract Bulletin written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1979 with Science categories.
An Investigation Of The Numerical Methods Of Finite Differences And Finite Elements For Digital Computer Solution Of The Transient Heat Conduction Diffusion Equation Using Optimum Implicit Formulations
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Author : Charles R. Martin (CAPT, USAF.)
language : en
Publisher:
Release Date : 1978
An Investigation Of The Numerical Methods Of Finite Differences And Finite Elements For Digital Computer Solution Of The Transient Heat Conduction Diffusion Equation Using Optimum Implicit Formulations written by Charles R. Martin (CAPT, USAF.) and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1978 with Finite differences categories.
Erda Energy Research Abstracts
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Author : United States. Energy Research and Development Administration
language : en
Publisher:
Release Date : 1977
Erda Energy Research Abstracts written by United States. Energy Research and Development Administration and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1977 with Power resources categories.
Selected Water Resources Abstracts
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Author :
language : en
Publisher:
Release Date : 1976
Selected Water Resources Abstracts written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1976 with Water categories.
Applied Mechanics Reviews
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Author :
language : en
Publisher:
Release Date : 1948
Applied Mechanics Reviews written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1948 with Mechanics, Applied categories.
Physics Briefs
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Author :
language : en
Publisher:
Release Date : 1990
Physics Briefs written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1990 with Physics categories.