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Title: A novel bubble function scheme for the finite element soulution of engineering flow problems
Author: Yazdani, Alireza
Awarding Body: Loughborough University
Current Institution: Loughborough University
Date of Award: 2007
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This thesis is devoted to the study of some difficulties of practical implementation of finite element solution of differential equations within the context of multi-scale engineering flow problems. In particular, stabilized finite elements and issues associated with computer implementation of these schemes are discussed and a novel technique towards practical implementation of such schemes is presented. The idea behind this novel technique is to introduce elemental shape functions of the polynomial forms that acquire higher degrees and are optimized at the element level, using the least squares minimization of the residual. This technique provides a practical scheme that improves the accuracy of the [mite element solution while using crude discretization. The method of residual free bubble functions is the point of our departure. Residual free bubble functions yield accurate solutions for the problems of different scales of amplitude in the variations of the field unknown. These functions, however, are not readily derivable and due to their complex forms, they are not usually significant from a practical point of view. Computation of a residual free bubble function involves the solution of the local residual differential equations, which can be as difficult as the solution of the original problem These will result in lack of flexibility or impracticality, especially in higher dimensions and non-symmetric problems. We benefit from the advantages of polynomials that are continuous, differentiable and easily integrated and derive practical polynomial bubble functions that approximate the residual free bubble functions, using the method of least squares minimization. We employ our technique to solve several problems and show its practicality and superiority over the c1assical linear finite elements.
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available