论文信息 - Generalized Petrov–Galerkin methods for the numerical solution of Burgers' equation

Generalized Petrov–Galerkin methods for the numerical solution of Burgers' equation

Generalized Petrov–Galerkin methods are applied in two different ways for the numerical solution of Burgers' equation. In the first place, it is used to produce upwinding in the way described by Mitchell and Griffiths.9,10 The main objective of this paper is in the second place to use it as a moving finite element method. In particular, it is shown that the methods of Miller and co-workers4–6 and Herbst et al.7,8 can be incorporated in the more general approach presented in this paper. Several choices for the test functions are discussed and numerical results are given.

David F. Griffiths | S. W. Schoombie | Ben M. Herbst | Andrew R. Mitchell

[1] C. D. Boor,et al. Good approximation by splines with variable knots. II , 1974 .

[2] Keith Miller,et al. Moving Finite Elements. I , 1981 .

[3] D. Spalding. A novel finite difference formulation for differential expressions involving both first and second derivatives , 1972 .

[4] Ben M. Herbst,et al. A moving Petrov‐Galerkin method for transport equations , 1982 .

[5] A. R. Mitchell,et al. Upwinding by Petron-Galerkin methods in convection-diffusion problems , 1980 .

[6] O. C. Zienkiewicz,et al. Finite element methods for second order differential equations with significant first derivatives , 1976 .

[7] Keith Miller,et al. The moving finite element method: Applications to general partial differential equations with multiple large gradients☆ , 1981 .

[8] A. R. Mitchell,et al. The Finite Difference Method in Partial Differential Equations , 1980 .