Schwarz methods for convection-diffusion problems

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

Volumn 1988, Issue , 2001, Pages 544-551

  Macmullen, H ^a   O'Riordan E ^a   Shishkin, G I ^b  

^a DUBLIN CITY UNIVERSITY   (Ireland)

^b INSTITUTE OF MATHEMATICS AND MECHANICS   (Russian Federation)

Author keywords

[No Author keywords available]

Indexed keywords

DIFFUSION IN LIQUIDS; HEAT CONVECTION; ITERATIVE METHODS;

CONVECTION DIFFUSION PROBLEMS; ITERATION COUNT; NUMBER OF ITERATIONS; NUMERICAL SOLUTION; PERTURBATION PARAMETERS; SCHWARZ METHOD; SINGULAR PERTURBATIONS; SINGULARLY PERTURBED;

CONVERGENCE OF NUMERICAL METHODS;

EID: 0011324039     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/3-540-45262-1_64     Document Type: Conference Paper

References (11)

1. Farrell, P. A., Boglaev, I. G., and Sirotkin, V. V.: Parallel domain decomposition methods for semi-linear singularly perturbed differential equations. Comput. Fluid Dynamic Journal 2 (4) (1994) 423–433
2. Farrell, P. A., Hegarty, A. F., Miller, J. J. H., O’Riordan, E., and Shishkin, G. I.: Robust Computational Techniques for Boundary Layers. Chapman and Hall/CRC Press, Boca Raton, U. S. A. (2000)
3. Garbey, M.: A Schwarz alternating procedure for singular perturtation problems. J. Sci. Comput. 17 (5) (1996) 1175–1201
4. Lube, G., Otto, F. C. and Muller, H.: A non-overlapping domain decomposition method for parabolic initial-boundary value problems. Appli. Numer. Math. 28 (1998) 359–369
5. MacMullen, H.: Schwarz domain decomposition methods for singularly perturbed differential equations. PhD thesis, Mathematical Sciences, D. C.U Dublin (2000)
6. MacMullen, H., Miller, J. J. H., O’Riordan E., and Shishkin, G. I.: Schwarz iterative methods for convection-diffusion problems with boundary layers. In: J. J. H. Miller and G.I Shishkin and L.G Vulkov eds. Analytical and Numerical Methods for Convection-Dominated and Singularly Perturbed Problems. Nova, New York (to appear)
7. MacMullen, H., Miller, J. J. H., O’Riordan E., and Shishkin, G. I.: A second order parameter-uniform overlapping Schwarz method for reaction-diffusion problems with boundary layers. J. Comput. Appl. Math. (to appear)
8. Mathew, T. P.: Uniform convergence of the Schwarz alternating method for solving singularly perturbed advection-diffusion equations. SIAM J. Numer. Anal. 35 (4) (1998) 1663–1683
9. Miller, J. J. H., O’Riordan, E., and Shishkin, G. I.: Fitted Numerical Methods for Singular Perturbation Problems. World Scientific Publishing Co., Singapore (1996)
10. Nataf, F. and Rogier, F.: Factorization of the convection-diffusion operator and the Schwarz algorithm. Math. Models Meth. Appli. Sci. 67 (1), (1995) 67–93
11. Quarteroni, A. and A. Valli, A.: Domain Decomposition Methods for Partial Differential Equations. Oxford University Press, (1999)