Continuous-time finite element analysis of multiphase flow in groundwater hydrology

IF 0.6 4区 数学 Q4 MATHEMATICS, APPLIED Applications of Mathematics Pub Date : 1994-07-01 DOI:10.21136/AM.1995.134291
Zhangxin Chen, M. Espedal, R. Ewing
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引用次数: 26

Abstract

Summary. A nonlinear differential system for describing an air-water system in ground water hydrology is given. The system is written in a fractional fl o w formulation, i.e., in terms o f a saturation and a gl oba l pressure. A continuous-time version o f the finite element method is developed and analyzed for the approximation o f the saturation and pressure. The saturation equation i s treated by a Galerkin finite element method, w h il e the pressure equation is treated by a mixed fi n i te element method. The analysis is carried out first for the case where the capillary diffusion coefficient is assumed to be uniformly positive, and is then extended to a degenerate case where the diffusion coefficient can be zero. It is shown that error estimates o f optimal order in the L 2 -norm and almost optimal order in the L °°- nor m can be obtained i n the nondegenerate case. In the degenerate case w e consider a regularization o f the saturation equation by perturbing the diffusion coefficient. The norm o f error estimates depends on the severity o f the degeneracy in diffusivity, with almost optimal order convergence for non-severe degeneracy. Existence and uniqueness o f the approximate solution is also proven.
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地下水水文多相流的连续有限元分析
总结。给出了描述地下水水文学中空气-水系统的非线性微分系统。该系统以分数形式表示,即饱和度和总压强。本文提出了一种连续时间有限元法,并对其进行了分析。饱和方程采用伽辽金有限元法处理,压力方程采用混合有限元法处理。首先对毛细管扩散系数为均匀正的情况进行了分析,然后将其推广到扩散系数为零的简并情况。结果表明,在非退化情况下,可以得到L°°- m范数的最优阶和L°°- m的几乎最优阶的误差估计。在退化情况下,我们考虑通过扰动扩散系数对饱和方程进行正则化。误差估计的范数取决于扩散率退化的严重程度,对于非严重退化具有几乎最优阶收敛性。并证明了近似解的存在唯一性。
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来源期刊
Applications of Mathematics
Applications of Mathematics 数学-应用数学
CiteScore
1.50
自引率
0.00%
发文量
0
审稿时长
3.0 months
期刊介绍: Applications of Mathematics publishes original high quality research papers that are directed towards applications of mathematical methods in various branches of science and engineering. The main topics covered include: - Mechanics of Solids; - Fluid Mechanics; - Electrical Engineering; - Solutions of Differential and Integral Equations; - Mathematical Physics; - Optimization; - Probability Mathematical Statistics. The journal is of interest to a wide audience of mathematicians, scientists and engineers concerned with the development of scientific computing, mathematical statistics and applicable mathematics in general.
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