Jim Douglas
Purdue University
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Featured researches published by Jim Douglas.
Siam Journal on Mathematical Analysis | 1990
Todd Arbogast; Jim Douglas; Ulrich Hornung
A general form of the double porosity model of single phase flow in a naturally fractured reservoir is derived from homogenization theory. The microscopic model consists of the usual equations describing Darcy flow in a reservoir, except that the porosity and permeability coefficients are highly discontinuous. Over the matrix domain, the coefficients are scaled by a parameter
Numerische Mathematik | 1988
Franco Brezzi; Jim Douglas
epsilon
Advances in Computers | 1961
Jim Douglas
representing the size of the matrix blocks. This scaling preserves the physics of the flow in the matrix as
Numerische Mathematik | 1999
Jim Douglas; Chieh Sen Huang; Felipe Pereira
epsilon
Numerische Mathematik | 1993
Jim Douglas; P. J. Paes Leme; Jean Elizabeth Roberts; Junping Wang
tends to zero. An effective macroscopic limit model is obtained that includes the usual Darcy equations in the matrix blocks and a similar equation for the fracture system that contains a term representing a source of fluid from the matrix. The convergence is shown by extracting weak limits in appropriate Hilbert spaces. A dilation operator is utilized to see the otherwise vanishing physics in the matrix blocks as
Computer Methods in Applied Mechanics and Engineering | 1991
Jim Douglas; Jeffrey L. Hensley; Todd Arbogast
epsilon
Mathematics and Computers in Simulation | 2006
Eduardo Abreu; Jim Douglas; Frederico Furtado; D. Marchesin; Felipe Pereira
tends to zero.
Transport in Porous Media | 1993
Jim Douglas; Todd Arbogast; Paulo Jorge Paes-leme; Jeffrey L. Hensley; Neci P. Nunes
SummaryThe solution of the Stokes problem is approximated by three stabilized mixed methods, one due to Hughes, Balestra, and Franca and the other two being variants of this procedure. In each case the bilinear form associated with the saddle-point problem of the standard mixed formulation is modified to become coercive over the finite element space. Error estimates are derived for each procedure.
Transport in Porous Media | 1991
Jim Douglas; Paulo Jorge Paes-leme; Jeffrey L. Hensley
Publisher Summary The chapter introduces the theoretical view of finite difference methods for approximating the solutions of partial differential equations of parabolic type. A few preliminary definitions and facts about difference analogues of derivatives are first presented. The symbols “u” and “w” will be used to denote the solution of a differential equation and the solution of a difference equation, respectively. Numerical treatment of parabolic differential equations is done by considering the boundary value problem for the heat equation in one space variable. The chapter begins by deriving the backward difference equation and the Crank-Nicolson difference equation. The local error in the time direction is decreased by deriving the Crank-Nicolson difference equation. Crank-Nicolson equations can be applied to problems for which slope conditions are specified at a boundary, but the disadvantage of the Crank-Nicolson method is that greater smoothness is required of the solution of the differential equation to insure convergence. The chapter deals with unconditionally unstable difference equations and higher order correct difference equations, and presents a comparison of the calculation requirements.
Archive | 1996
Zhangxin Chen; Jim Douglas
Summary. The MMOC procedure for approximating the solutions of transport-dominated diffusion problems does not automatically preserve integral conservation laws, leading to (mass) balance errors in many kinds of flow problems. The variant, called the MMOCAA, discussed herein preserves the conservation law at a minor additional computational cost. It is shown that its solution, in either Galerkin or finite difference form, converges at the same rates as were proved earlier by Douglnas and Russell for the standard MMOC procedure.