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Analise van die eindige elementmetode vir parsiele differensiaalvergelykings met dinamiese randvoorwaardes

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dc.contributor.advisor van Rensburg NFJ, Dr en
dc.contributor.author Geldenhuys JJ en
dc.date.accessioned 2016-09-26T06:27:47Z
dc.date.available 2016-09-26T06:27:47Z
dc.date.submitted 1993 en
dc.identifier.uri http://hdl.handle.net/20.500.11892/174410
dc.description.abstract When physical processes such as heat transfer or the vibration of elastic bodies are modelled, the result is partial differential equations with boundary conditions. The boundary conditions are supposed to reflect the behaviour of the surrounding material. Efforts to create more realistic mathematical models result in the appearance of time derivatives in the boundary conditions. These so called dynamical boundary conditions contain also high order tangential derivatives. The equilibrium condition of these time-dependent problems is modelled by elliptic problems with the same tangential derivatives in the boundary conditions. Vibration analysis result in eigenvalue problems. For the new type of problem eigenvalues as well as high order tangential derivatives appear in the boundary conditions. All four types of problems mentioned are relatively new to the theory of partial differential equations and the analysis of the solvability received due attention for the last fifteen years. The purpose of this investigation was to determine the appliability of the finite element method to solve these problems. The focus was on the discretization of the problem by the Galerkin technique and the subsequent analysis of the convergence of the approximate solution. Due to geometrical consideration the investigation was restricted to problems in two (spatial) dimensions. It turned out that the discrete version of all the problems was exactly the same as corresponding problems with conventional boundary conditions. This made an analysis of numerical techniques superfluous. Although the variational form of the problem is in the product of two Sobolev spaces, it was possible to deduce convergence results analogous to those for corresponding problems with conventional boundary conditions. The fact that the analysis of convergence was carried out for a product space necessitated the development of an interpolation theory for product spaces. To generate numerical results with the aid of a computer was supplementary to the purpose of the investigation. Only one problem could be found which was directly comparable. In this case numerical results compared well. In other cases the results had to be compared to solutions of different problems modelling approximately the same situation. The results proved to be realistic. en
dc.language Afrikaans en
dc.subject Mathematics, mathematical statistics and statistics en
dc.subject Differential and integral equations en
dc.title Analise van die eindige elementmetode vir parsiele differensiaalvergelykings met dinamiese randvoorwaardes en
dc.type Doctoral degree en
dc.description.degree PhD en


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