IMPLEMENTATION OF MIXED METHODS AS FINITE DIFFERENCE METHODS AND APPLICATIONS TO NONISOTHERMAL MULTIPHASE FLOW IN POROUS MEDIA

• 来源期刊: 计算数学（英文版）
• 关键词: Finite difference Implementation Mixed method Error estimates Superconvergence Tensor coefficient Nonisothermal multiphase Multicom ponent flow Porousmedia.
• 年，卷（期）: 2006,（3）
• 页码范围: 281-294
• 页数: 14页
• 语种: 英文

摘要

In this paper we consider mixed finite element methods for second order elliptic problems. In the case of the lowest order Brezzi-Douglás-Marini elements (if d = 2) or Brezzi--Douglás-Fortin element(if d =3) on rectangular parallelepipeds, we show that the mixed method system, by incorporating certain quadrature rules, can be written as asimple, cell-centered finite difference method. This leads to the solution of a sparse, positive semidefinite linear system for the scalar unknown. For a diagonal tensor coefficient,the sparsity pattern for the scalar unknown is a five point stencil if d = 2, and seven ifd = 3. For a general tensor coefficient, it is a nine point stencil, and nineteen, respectively.Applications of the mixed method implementation as finite differences to nonisothermal multiphase, multicomponent flow in porous media are presented.