数学季刊 ›› 2013, Vol. 28 ›› Issue (1): 60-68.

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半线性双曲波动方程的H1-Galerkin扩展混合元方法

  

  1. 1. School of Statistics and Mathematics, Inner Mongolia University of Finance and Economics 2. School of Mathematical Sciences, Inner Mongolia University 

  • 收稿日期:2011-04-17 出版日期:2013-03-30 发布日期:2023-03-08
  • 作者简介:WANG Jin-feng(1980-), female, native of Huludao, Liaoning, a lecturer of Inner Mongolia University of Finance and Economics, engages in the theories and numerical methods for differential equations; LIU Yang(1980-), male(Manzu), native of Tieling, Liaoning, a lecturer of Inner Mongolia University, Ph.D., engages in the numerical methods for differential equations; LI Hong(1973-), female, native of Tongliao, Inner Mongolia, a professor of Inner Mongolia University, Ph.D., engages in the numerical methods for differential equation.
  • 基金资助:
    Supported by the National Natural Science Fund(11061021)； Supported by the Scientific Research Projection of Higher Schools of Inner Mongolia(NJZZ12011, NJ10006)； Supported by the Program of Higher-level talents of Inner Mongolia University(125119)； Supported by the Scientific Research Projection of Inner Mongolia University of Finance and Economics(KY1101)

An H1-Galerkin Expanded Mixed Element Method for Semi-linear Hyperbolic Wave Equation

  1. 1. School of Statistics and Mathematics, Inner Mongolia University of Finance and Economics 2. School of Mathematical Sciences, Inner Mongolia University 

  • Received:2011-04-17 Online:2013-03-30 Published:2023-03-08
  • About author:WANG Jin-feng(1980-), female, native of Huludao, Liaoning, a lecturer of Inner Mongolia University of Finance and Economics, engages in the theories and numerical methods for differential equations; LIU Yang(1980-), male(Manzu), native of Tieling, Liaoning, a lecturer of Inner Mongolia University, Ph.D., engages in the numerical methods for differential equations; LI Hong(1973-), female, native of Tongliao, Inner Mongolia, a professor of Inner Mongolia University, Ph.D., engages in the numerical methods for differential equation.
  • Supported by:
    Supported by the National Natural Science Fund(11061021)； Supported by the Scientific Research Projection of Higher Schools of Inner Mongolia(NJZZ12011, NJ10006)； Supported by the Program of Higher-level talents of Inner Mongolia University(125119)； Supported by the Scientific Research Projection of Inner Mongolia University of Finance and Economics(KY1101)

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摘要： An H1-Galerkin expanded mixed finite element method is discussed for a class of second order semi-linear hyperbolic wave equations. By using the mixed formulation, we can get the optimal approximation for three variables: the scalar unknown, its gradient and its flux(coefficient times the gradient), simultaneously. We also prove the existence and uniqueness of semi-discrete solution. Finally, we obtain some numerical results to illustrate the efficiency of the method.

关键词: hyperbolic wave equations, semi-linear, H1-Galerkin expanded mixed method; existence and uniqueness, error estimates

Abstract: An H1-Galerkin expanded mixed finite element method is discussed for a class of second order semi-linear hyperbolic wave equations. By using the mixed formulation, we can get the optimal approximation for three variables: the scalar unknown, its gradient and its flux(coefficient times the gradient), simultaneously. We also prove the existence and uniqueness of semi-discrete solution. Finally, we obtain some numerical results to illustrate the efficiency of the method.

Key words: hyperbolic wave equations, semi-linear, H1-Galerkin expanded mixed method, existence and uniqueness, error estimates

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