On the robust exponential convergence of hp finite element methods for problems with boundary layers

IMA Journal of Numerical Analysis

Volumn 17, Issue 4, 1997, Pages 577-601

  Melenk, Jens Markus ^a  

^a ETH ZURICH   (Switzerland)

Author keywords

[No Author keywords available]

Indexed keywords

BOUNDARY LAYERS; INPUT OUTPUT PROGRAMS;

EXPONENTIAL CONVERGENCE; EXPONENTIAL RATES; HP VERSION OF THE FINITE ELEMENT METHODS; HP-FINITE ELEMENT METHODS; MODEL PROBLEMS; PERTURBATION PARAMETERS; PIECEWISE POLYNOMIALS; SINGULARLY PERTURBED;

FINITE ELEMENT METHOD;

EID: 0031508702     PISSN: 02724979     EISSN: None     Source Type: Journal    
DOI: 10.1093/imanum/17.4.577     Document Type: Article

References (11)

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2. CIARLET, P. G. 1978 The Finite Element Method for Elliptic Problems. Amsterdam: North-Holland.
3. DAVIS, P. J. 1974 Interpolation and Approximation. New York: Dover.
4. MELENK, J. M., & SCHWAB, C. 1997a hp FEM for reaction-diffusion equations. Part I: robust exponential convergence. Part II: regularity. Research Reports 97-03 and 97-04, Seminar für Angewandte Mathematik, ETH Zürich, CH-8092 Zürich, Switzerland.
5. MELENK, J. M., & SCHWAB, C. 1997b An hp finite element method for convection-diffusion problems. Research Report 97-05, Seminar für Angewandte Mathematik, ETH Zürich, CH-8092 Zürich, Switzerland.
6. MILLER, J. J. H., O'RIORDAN, E., & SHISHKIN, G. I. 1996 Fitted Numerical Methods for Singular Perturbation Problems. Singapore: World Scientific.
7. MORTON, K. W. 1996 Numerical Solution of Convection-diffusion Problems. London: Chapman & Hall.
8. O'RIORDAN, E., & STYNES, M. 1986 A uniformly accurate finite-element method for a singularly perturbed one-dimensional reaction-diffusion problem. Math. Comput. 47, 555-70.
9. ROOS, H.-G., STYNES, M., & TOBISKA, L. 1996 Numerical Methods for Singularly Perturbed Differential Equations. Berlin: Springer.
10. SCHWAB, C., & SURI, M. 1996 The p and hp version of the finite element method for a problem with boundary layers. Math. Comput. 65, 1403-29.
11. SÜNDERMANN, B. 1980 Lebesgue constants in Lagrangian interpolation at the Fekete points. Ergebnisberichte der Lehrstühle Mathematik III & VIII (Angewandte Mathematik) 44, Universität Dortmund.