Sine-Gordon方程的混合有限体积元方法及数值模拟

Abstract

Abstract: The mixed finite volume element method for the one-dimensional sine-Gordon equation with Dirichlet or Neumann boundary conditions is developed and studied. By introducing a transfer operator γ_h which maps the trial function space into the test function space and combining mixed finite element with finite volume method, the continuous-in-time, explicit-in-time and implicit-in-time mixed finite volume element schemes are constructed. Stability analysis for explicit-in-time scheme is given, and optimal error estimates for three schemes are obtained. Finally, numerical experiments are given to verify the theoretical results and the effectiveness of the proposed schemes.

Key words: Sine-Gordon equation, Mixed finite volume element method, Optimal error estimate

CLC Number:

O242.21

Fang Zhichao, Li Hong, Luo Zhendong, Liu Yang. Mixed Finite Volume Element Method and Numerical Simulation for Sine-Gordon Equation[J].Acta mathematica scientia,Series A, 2018, 38(2): 395-416.

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References

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Mixed Finite Volume Element Method and Numerical Simulation for Sine-Gordon Equation

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