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S. Feldberg, C. Goldstein, Manfred Rudolph (1996)
A stability criterion for accurate simulation of electrochemical diffusion-kinetic phenomena at the rotating disk electrode and implications for simulation of diffusion-migration and other problemsJournal of Electroanalytical Chemistry, 413
G. Lube (1992)
Streamline diffusion finite element method for quasilinear elliptic problemsNumerische Mathematik, 61
X. Cai, W. Gropp, D. Keyes (1992)
Comparison of some domain decomposition algorithms for nonsymmetric elliptic problems
J. Lions, E. Magenes (1972)
Non-homogeneous boundary value problems and applications
A. Brooks, T. Hughes (1990)
Streamline upwind/Petrov-Galerkin formulations for convection dominated flows with particular emphasis on the incompressible Navier-Stokes equationsComputer Methods in Applied Mechanics and Engineering, 32
C. Goldstein, S. Parter (1988)
On the norm equivalence of singularly pertubed elliptic difference operatorsApplied Mathematics and Computation, 26
S. Eisenstat, H. Elman, M. Schultz (1983)
Variational Iterative Methods for Nonsymmetric Systems of Linear EquationsSIAM Journal on Numerical Analysis, 20
H. Elman, M. Schultz (1986)
Preconditioning by fast direct methods for nonself-adjoint nonseparable elliptic equationsSIAM Journal on Numerical Analysis, 23
Y. Saad, M. Schultz (1986)
GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systemsSiam Journal on Scientific and Statistical Computing, 7
A. Brandt (1977)
Multi-level adaptive solutions to boundary-value problems math comptr
A. Bayliss, C. Goldstein, Eli Turkel (1983)
An Iterative method for the Helmholtz equationJournal of Computational Physics, 49
A. Bayliss, C. Goldstein, Eli Turkel (1985)
THE NUMERICAL SOLUTION OF THE HELMHOLTZ EQUATION FOR WAVE PROPAGATION PROBLEMS IN UNDERWATER ACOUSTICSComputers & Mathematics With Applications, 11
X. Cai, O. Widlund (2017)
Domain Decomposition Algorithms for Indefinite Elliptic ProblemsSIAM J. Sci. Comput., 13
H. Elman (1982)
Iterative methods for large, sparse, nonsymmetric systems of linear equations
C. Goldstein (1991)
Preconditioning singularity perturbed elliptic and parabolic problemsSIAM Journal on Numerical Analysis, 28
J. Mandel, S. McCormick, R. Bank (1987)
5. Variational Multigrid Theory
Claes Johnson, A. Schatz, L. Wahlbin (1987)
Crosswind Smear and Pointwise Errors in Streamline Diffusion Finite Element MethodsMathematics of Computation, 49
This paper is concerned with the numerical solution ofmultidimensional convection dominated convectiondiffusionproblems. These problems are characterized by a large parameter, K,multiplying the convection terms. The goal of this work is the developmentand analysis of effective preconditioners for iteratively solving the largesystem of linear equations arising from various finite element and finitedifference discretizations with grid size h. When centered finitedifference schemes and standard Galerkin finite element methods are used,h must be related to K by the stability constraint, Kh C0, where the constant C0 is sufficiently small. A class ofpreconditioners is developed that significantly reduces the condition numberfor large K and small h. Furthermore, these preconditioners areinexpensive to implement and well suited for parallel computation. It isshown that under suitable assumptions, the number of iterations remainsbounded as h 0 with K fixed and, at worst, grows slowly as K. Numerical results are presented illustrating the theory. Itis also shown how to apply the theoretical results to more generalconvectiondiffusion problems and alternative discretizationsincluding streamline diffusion methods that remain stable as Kh.
International Journal of Numerical Methods for Heat and Fluid Flow – Emerald Publishing
Published: Feb 1, 1995
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