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Discontinuous Finite Volume Method For Several Kinds Of Evolution Equations

Posted on:2011-01-06Degree:MasterType:Thesis
Country:ChinaCandidate:Y ShaoFull Text:PDF
GTID:2120360308964955Subject:Computational Mathematics
Abstract/Summary:PDF Full Text Request
In this paper, the following advection-diffusion initial boundary value problem is simulated by a new method called characteristic discontinuous finite volume method, which is a combination of characteristic method and discontinuous finite volume method proposed by Xiu Ye. Our analysis shows that the new method not only inherits the advantages of discontinuous finite volume method, for example, high order accuracy, parallelizability and simplicity of space construction, it also possess some features of characteristic method:it is stable and can smear sharp fronts of the solution.So it's a new and effective method for advection-diffusion problem. In this chapter, we prove the existence and uniqueness of the solution and stability of the procedures we proposed. By making the numerical analysis, we obtain the optimal error estimates of L2-norm and |||·|||1,h-norm about the unknown function.Then we simulate the following second-order nonlinear parabolic problem by discontinuous finite volume method based on Chunjia Bi's work about parabolic problem. The semi discretization and fully discretization discontinuous finite volume procedures for this problem are proposed. And we propose the auxiliary formula-tion and give the error analysis. Numerical analysis shows that we can obtain the optimal error estimates of L2-norm and|||·|||1,h-norm about the unknown function by this method.
Keywords/Search Tags:advection-diffusion problem, nonlinear parabolic problem, discontinuous finite volume method, characteristic discontinuous finite volume method, optimal error estimate
PDF Full Text Request
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