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A-posteriori error analysis and adaptive finite element methods for singularly perturbed convection-diffusion equations. (English) Zbl 0489.65056


MSC:

65L10 Numerical solution of boundary value problems involving ordinary differential equations
65L60 Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations
65L50 Mesh generation, refinement, and adaptive methods for ordinary differential equations
34D15 Singular perturbations of ordinary differential equations
34B05 Linear boundary value problems for ordinary differential equations
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References:

[1] Babuška, Error estimates for adaptive finite element computations, SIAM J. Numer. Anal. 15 pp 736– (1978) · Zbl 0398.65069 · doi:10.1137/0715049
[2] Babuška, Analysis of optimal finite element meshes in R1, Math. Comp. 33 pp 435– (1979)
[3] Babuška, A posteriori error analysis of finite element solutions for one-dimensional problems, SIAM J. Numer. Anal. 18 pp 565– (1981) · Zbl 0487.65060 · doi:10.1137/0718036
[4] Babuška, An error analysis for the finite element method applied to convection diffusion problems (1981)
[5] Barrett, Optimal finite element solutions to diffusion-convection problems in one dimension, Internat. J. Numer. Methods Engrg. 15 pp 1457– (1980) · Zbl 0442.76069 · doi:10.1002/nme.1620151004
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[8] de Groen, A finite element method with a large mesh-width for a stiff boundary value problem, J. Comput. Appl. Math. 7 pp 3– (1981) · Zbl 0452.65056 · doi:10.1016/0771-050X(81)90001-2
[9] van Harten, Nonlinear singular perturbation problems: Proofs of correctness of a formal approximation based on a contraction principle in a Banach space, J. Math. Anal. Appl. 65 pp 126– (1978) · Zbl 0393.34037 · doi:10.1016/0022-247X(78)90206-8
[10] Kreiss, Numerical methods for singular perturbation problems, SIAM J. Numer. Anal. 18 pp 262– (1981) · Zbl 0457.65064 · doi:10.1137/0718019
[11] Reinhardt, A posteriori error estimates for the finite element solution of a singularly perturbed linear ordinary differential equation, SIAM J. Numer. Anal. 18 pp 406– (1981) · Zbl 0467.65034 · doi:10.1137/0718027
[12] Reinhardt, Analytical and numerical approaches to asymptotic problems in analysis (Proc. Conf. Univ. of Nijmegen, Nijmegen, June 1980) pp 213– (1981) · doi:10.1016/S0304-0208(08)71111-3
[13] Mathematic Studies 47
[14] Reinhardt , H.-J. Analysis of adaptive finite element methods for - {\(\epsilon\)}u” + u’=fbased on a-posteriori error estimates 1981
[15] Rheinboldt, On a theory of mesh-refinement processes, SIAM J. Numer. Anal. 17 pp 766– (1980) · Zbl 0472.65009 · doi:10.1137/0717064
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