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The Study With DG-FEM For Convection-diffusion Equation

Posted on:2010-08-09Degree:MasterType:Thesis
Country:ChinaCandidate:H J XuFull Text:PDF
GTID:2120360275498148Subject:Computational Mathematics
Abstract/Summary:PDF Full Text Request
A large number of convection and diffusion phenomenons have happened in Nature and other engine fields Such as:environmental science,energy exploitation,fluid mechanics, electronics,and so on.Therefore,the study of the numerical solution method for convection diffusion problems is important in theoretical and practical.In this paper,From the basic principle of discontinuous Finite Elements,we constructed the discontinuous finite element numerical method about the convection-diffusion equation,and stuy the adptive methods for convection-diffusion equation,and give a numerical experiments for the ploblem.Experimental Comparison of adaptive methods and non-adaptive methods of CPUtime and the convergence rate,From the results we can see that adaptive method to speed up the convergence rate significantly,and shows adaptive efficiency.Also as a result of the numerical solution of partial differential equations reduced to the solution of linear systems,Therefore,in this paper,a kind of new algorithm on solving block penta-diagonal linear systems is proposed,and prove the reliability and stability of the method.It is a direct scheme and can avoid accumulated error resulted by iterative methods.Value results have illustrated that our algorithm has high precision.
Keywords/Search Tags:convection-diffusion equation, discontinuous Finite Elements, adaptive methods, LSERK methods, Mixed finite element method, Block penta-diagonal matrix
PDF Full Text Request
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