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Finite Volume Element Method For Two Kinds Of Equations

Posted on:2013-03-06Degree:MasterType:Thesis
Country:ChinaCandidate:S F LiFull Text:PDF
GTID:2230330371969282Subject:Computational Mathematics
Abstract/Summary:PDF Full Text Request
In this paper, the following two-dimensional convection-difusion initial bound-ary problemis simulated by a new method called modified characteristic discontinuous finitevolume element method. As we know, characteristic discontinuous finite volumemethod, which not only possess the advantages of discontinuous finite volume method,for example, high order accuracy, parallelizability and simplicity of space construc-tion, it also inherits some features of characteristic method: it is stable and cansmear sharp front of the solution. But the characteristic discontinuous finite vol-ume method does not have the conservation of nature, Therefore, in the secondchapter, we first simulate the modified characteristic discontinuous finite volumeelement method, by integralling in the dual space unit, the method not only hasthe characteristics of discontinuous finite volume element method, while maintain-ing the discontinuous finite volume element method for the characteristics of localconservation of mass, by making the numerical analysis, we obtain the optimal errorestimates of |||ยท|||1,h-norm about the unknow function. In the third chapter, the following stokes equation is considered.The finite volume procedures for this problem are proposed. Finite volume elementmethod can make the equation in the control volume to maintain conservation law,which is an important physical properties, while the calculation of the format issimple, small amount of computation. It is an efective method to Solve the partialdiferential equation . Using of the method of stream function-vorticity, we get theoptimal order in the H1and L2norm error estimates of the stream function andvorticity, and the optimal order L2norm error estimates of the velocity field havebeen derived.
Keywords/Search Tags:convection-diffusion equation, conservation characteristics of discontinuous finite volume element, unsteady stokes problem, finite volume element method, error estimate
PDF Full Text Request
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