A Continuous Space-Time Mixed Finite Element Method for Sine-Gordon Equations

WANG Chunyuan; LI Hong; HE Siriguleng

doi:10.21656/1000-0887.440293

Volume 45 Issue 4

Apr. 2024

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WANG Chunyuan, LI Hong, HE Siriguleng. A Continuous Space-Time Mixed Finite Element Method for Sine-Gordon Equations[J]. Applied Mathematics and Mechanics, 2024, 45(4): 490-501. doi: 10.21656/1000-0887.440293

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A Continuous Space-Time Mixed Finite Element Method for Sine-Gordon Equations

doi: 10.21656/1000-0887.440293

1.
School of Mathematical Sciences, Inner Mongolia University, Hohhot 010021, P.R.China
2.
School of Mathematical Sciences, Hohhot Minzu College, Hohhot 010051, P.R.China

Received Date: 2023-09-27
Rev Recd Date: 2023-11-28
Publish Date: 2024-04-01

Abstract

Abstract

The mixed finite element method was combined with the continuous space-time finite element method to construct a continuous space-time mixed finite element scheme for sine-Gordon equations, through the introduction of independent variable p=u_t to solve the equations. This scheme uses the finite element method to treat both time and space variables. The space-time mixed finite element scheme can reduce the order of the equation and lower the smoothness requirements on the finite element space. The advantages of the finite element method was utilized in both the time and the space directions, thereby to obtain high-precision space-time numerical solutions. The stability of numerical solutions was strictly proven in the theoretical analysis, and error estimates for u and p were provided. Finally, the effectiveness and feasibility of the proposed method were demonstrated through numerical examples.
- sine-Gordon equation,
- continuous space-time mixed finite element method,
- stability,
- error estimate

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References(16)

References

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