摘要
在地学中广泛应用的偏微分方程数值解法有两种:有限差分法及有限单元法。对于定常态问题两种方法完全等价,对于非定常态问题有限单元法形成的代数方程归根到底仍是有限差分方程,但在一定条件下会引起反常问题,原因是与代数组相容的不是原来的热传导方程,而是反热传导方程。
A number of phenomena and processes in geosciences can be summarized by second order partial differential equations. The major numerical methods for their snlution include the classical finite difference method and the finite element method newly developed in the past two lecades. Since 1977 the author has proved that for Laplace and Poisson esuations, these two (?)ethods are identical, and they are different only in the process of formulation. For transient (?)oblems, such as heat conduction in the earth and groundwater and oil-gas unsteady flow in rous media, there are some differences in resulting linear algebraic equations. In general, (?)o methnds give similar results, but when time step is decreased to some extent, the resulting (?)ebraic equations will be consistent with the anti-heat conduction equation rather than the (?)iginal heat conduction equations. This is the reason why unrealistic potentials are produced by the finite element method. Such a problem can be overcome by using the lumped mass procedure, but it makes two methods identical again.To improve the traditional finite difference method, it is guite desirable and convenient to introduce the common practice of the finite element method to define the parameters in elements rather than on nodes.
出处
《地质学报》
EI
CAS
CSCD
北大核心
1993年第3期266-275,共10页
Acta Geologica Sinica
关键词
地质学
偏微分方程
数值解法
partial differential equation, numerical solution, finite element method, finite difference method
