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Stabilizing Discontinuous Galerkin Method for Solving Parabolic Equations

Author: ZhaoJuan
Tutor: GeZhiZuo
School: Henan University
Course: Computational Mathematics
Keywords: Discontinuous Galerkin method Semidiscrete formulation Back-ward Euler discretization Forward Euler discretization Crank-Nicolson discretization apriori error analysis
CLC: O241.82
Type: Master's thesis
Year: 2013
Downloads: 13
Quote: 0
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Abstract


The thesis proposes a stabilizact Discontinuous Galerkin method with penalty termsin Broken Sobolev space. The method content the numerical stability and also the localconservativeness.It adopts a Discontinuous Galerkin method with penalty terms to this thesis fromthe perspective of space. A priori error analysis is also given and the optimal degreeof convergence is also obtained. The thesis will discrete the above formulation by usingForward Euler method, Backward Euler method, and Crank-Nicolson method from theperspective of time. A priori error analysis is also given and the optimal degree of con-vergence is also obtained.It gives a specifc numerical example at the end of the thesis.Then an expected result is obtained by using Freefem++.

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CLC: > Mathematical sciences and chemical > Mathematics > Computational Mathematics > Numerical Analysis > The numerical solution of differential equations, integral equations > Numerical Solution of Partial Differential Equations
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