Quasioptimal uniformly convergent finite element methods for the elliptic boundary layer problem

Computers and Mathematics with Applications

Volumn 33, Issue 10, 1997, Pages 11-22

  Li, J ^a  

^a FLORIDA STATE UNIVERSITY   (United States)

Author keywords

Elliptic partial differential equations; Finite element methods; Singularly perturbed problems

Indexed keywords

BOUNDARY VALUE PROBLEMS; PARTIAL DIFFERENTIAL EQUATIONS;

ELLIPTIC PARTIAL DIFFERENTIAL EQUATIONS; SINGULARLY PERTURBED PROBLEMS;

FINITE ELEMENT METHOD;

EID: 0031128557     PISSN: 08981221     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0898-1221(97)00073-4     Document Type: Article

References (16)

1. th European Multigrid Conference, (Edited by P.W. Hemker et al.), pp. 1-19, Basel, (1994).
2. Y. Su, Boundary Layer Correction Method for Singularly Perturbed Problems, (in Chinese), Shanghai Science and Technology Press, Shanghai, (1983).
3. R.P. Doolan, J.J.H. Miller and W.H.A. Schilders, Uniform Numerical Methods for Problems with Initial and Boundary Layers, Boole Press, Dublin, (1980).
4. H.-G. Roos, Ten ways to generate the Il'in and related schemes, J. Comput. Appl. Math. 53, 43-59, (1994).
5. C. Johnson, A.H. Schatz and L.B. Wahlbin, Crosswind smear and pointwise errors in streamline diffusion finite element methods, Math. Comp. 49, 25-38, (1987).
6. E. O'Riordan and M. Stynes, A globally convergent finite element method for a singularly perturbed elliptic problem in two dimensions, Math. Comp. 57, 47-62, (1991).
7. G.I. Shishkin, Grid approximation of singularly perturbed parabolic equations with internal layers, Sov. J. Numer. Anal. Math. Modelling 3, 393-407, (1988).
8. G. Sun and M. Stynes, Finite element methods for singularly perturbed high-order elliptic two-point boundary value problems. I: Reaction-diffusion-type problems, IMA J. Numer. Anal. 15, 117-139, (1995).
9. E.C. Gartland, Jr., Graded-mesh difference schemes for singularly perturbed two-point boundary value problems, Math. Comp. 51, 631-657, (1988).
10. Q. Wu and J. Li, Numerical methods for parabolic equation with a small parameter in time variable, (English), Appl. Math. Mech. 12, 733-740, (1991).
11. Q. Wu and J. Li, Numerical solutions for singularly perturbed semi-linear parabolic equations, (English), Appl. Math. Mech. 14, 793-801, (1993).
12. P.G. Ciarlet, Basic error estimates for elliptic problems, In Handbook of Numer. Anal., (Edited by P.G. Ciarlet and J.L. Lions), Volume II, pp. 16-351, North-Holland, Amsterdam, (1991).
13. D. Gilberg and N. Trudinger, Elliptic Partial Differential Equations of Second Order, Springer, (1977).
14. G. Strang and G.J. Fix, An Analysis of the Finite Element Method, Prentice Hall, Englewood Cliffs, NJ, (1973).
15. M.H. Schultz, Spline Analysis, Prentice Hall, New York, (1973).
16. H.-G. Roos, Necessary convergence conditions for upwind schemes in the two-dimensional case, Int. J. Numer. Methods Engrg. 21, 1459-1469, (1985).