by Richard L. Cooley
Abstract
Introduction
Purpose and scope
Acknowledgment
Finite-element formulation in Cartesian coordinates
Governing flow equation and boundary conditions
Finite-element discretization
Derivation of finite-element equations
Error-functional justification for the finite-element equations
Integral approximations
Rotation of coordinate axes
Evaluation of spatial integrals
Example of equation assembly
Evaluation of time integral
Mass-balance calculation
Extensions of the basic equations
Unconfined flow
Drying and resaturation of nodes
Combined confined and unconfined flow
Point head-dependent discharge (springs and drainage wells)
Areal head-dependent leakage combined with aquifer dewatering
Areal head-dependent discharge (evapotranspiration)
Line head-dependent leakage combined with aquifer dewatering
Leakage of water stored elastically in a confining unit (transient leakage)
Finite-element formulation in axisymmetric cylindrical coordinates
Governing flow equation and boundary conditions
Finite-element discretization
Derivation of finite-element equations
Finite-element formulation for steady-state flow
Linear case
Nonlinear case
Solution of matrix equations
Definition of matrix equation
Symmetric-Doolittle method
Modified incomplete-Cholesky conjugate-gradient method
Generalized conjugate-gradient method
Modified incomplete-Cholesky factorization
Stopping criteria
Comparisons of numerical results with analytical solutions
Theis solution of unsteady radial flow to a pumped well
Hantush solution of unsteady radial flow to a pumped well in a leaky aquifer
Moench and Prickett solution for conversion from confined to unconfined flow near a pumped well
Steady-state flow through a dam with areal recharge
Two-dimensional steady-state flow in an unconfined aquifer
Summary
References cited
Appendix A
Notation
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