论文信息 - A moving Petrov‐Galerkin method for transport equations

A moving Petrov‐Galerkin method for transport equations

A time-dependent transport equation is solved numerically by using a Petrov-Galerkin technique on a time-dependent grid. A piecewise linear trial solution and piecewise Hermite cubic test functions are used. The same method is also applied to a time-independent problem, in which case it automatically generates a grid in a way which bears some resemblance to certain existing grid-generation techniques. Several numerical examples are given.

Ben M. Herbst | B. Herbst | A. R. Mitchell | Andrew R. Mitchell | S. W. Schoomnbie

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

[2] J. Cole. On a quasi-linear parabolic equation occurring in aerodynamics , 1951 .

[3] R. Russell,et al. Adaptive Mesh Selection Strategies for Solving Boundary Value Problems , 1978 .

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

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

[6] Victor Pereyra,et al. Mesh selection for discrete solution of boundary problems in ordinary differential equations , 1974 .

[7] V. Pereyra,et al. An adaptive finite difference solver for nonlinear two point boundary problems with mild boundary layers. , 1975 .

[8] J. A. White,et al. On Selection of Equidistributing Meshes for Two-Point Boundary-Value Problems , 1979 .