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The Finite Element Methods For Two Kinds Of Evolution Equations

Posted on:2008-03-10Degree:MasterType:Thesis
Country:ChinaCandidate:A Q LiFull Text:PDF
GTID:2120360242960410Subject:Applied Mathematics
Abstract/Summary:PDF Full Text Request
In this paper, we consider the Characteristics-Finite Volume Element Methodfor the convection dominated diffusion equation and Expanded Mixed Finite ElementMethod for the initial-value problems of purely longtudinal motion of a humogeneousbar, and obtained the error estimates of this two discrete solutions.In chapter one, we consider the Characteristics-Finite Volume Element Methodfor the following convection dominated diffusion equationTheoretical analysis indicates that the method is effective and has optimal error esti-mates in L~2 and H~1 norm.In chapter two, we consider the Expanded Mixed Finite Element Method for thefollowing initial-value problems of purely longtudinal motion of a humogeneous barWe present the error analysis of the solutions of the expanded mixed finite elementscheme and derive optimal error estimates for the discrete scheme in L~2-norm and inH~1-norm.
Keywords/Search Tags:convection dominated diffusion equation, the initial-value problems of purely longtudinal motion of a humogeneous bar, characteristics-finite volume element method, expanded mixed finite element method, error estimate
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