Abstract
The paper describes computable local a posteriori error estimates for the numerical solution of convection-dominated boundary-value problems. Being applied to singularly perturbed elliptic equations, the obtained estimates are uniform w.r.t. the small parameter. Moreover, if quadrature errors are neglected the numerical approximation of the theoretical error bounds preserves the relation signs in the estimates.
Zusammefassung
Die Arbeit beschreibt berechenbare lokale a posteriori Fehlerabschätzungen für die numerischen Lösung konvektionsdominanter Randwertaufgaben. Bei Anwendung auf singulär gestörte Gleichungen erweisen sich die gewonnenen Abschätzungen als gleichmäßig bzgl. des kleinen Parameters. Wird ferner der Quadraturfehler vernachlässigt, konserviert die numerische Approximation der theoretischen Schranken die Relationszeichen in den Abschätzungen.
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Ainsworth, M., Oden, J. T.: A posteriori error estimator for second order elliptic systems. Part I. The theoretical foundations and a posteriori error analysis. Comput. Math. Appl.25, 101–113 (1993).
Ainsworth, M., Oden, J. T.: The unified approach to a posteriori error estimation using element residual methods. Numer Math.65, 23–50 (1993).
Angermann, L.: Computable estimation of error indicators associated with local boundary value problems. Informationen der TU Dresden 07-04-91, TU Dresen, 1991.
Angermann, L.: An a-posteriori estimation for the solution of elliptic boundary value problems by means of upwind FEM. IMA J. Numer. Anal.12, 201–215 (1992).
Angermann, L.: Error estimates for the finite-element solution of an elliptic singularly perturbed problem. IMAA J. Numer. Anal.15, 161–196 (1995).
Babuška, I., Rheinboldt, W. C.: Error estimates for adaptive finite element computation. SIAM J. Numer. Anal.15, 736–754 (1978).
Eriksson, K., Johnson, C.: Adaptive streamline diffusion finite element methods for stationary convection-diffusion problems. Math. Comp.60, 167–188 (1993).
Gilbarg, D., Trudinger, N. S., Elliptic partial differential equations of second order. Berlin, Heidelberg, New York, Tokyo: Springer, 1983.
Vacek, J.: Dual variational principles for an elliptic defferential equation. Aplikace Matematiky,21, 5–27 (1976).
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Angermann, L. Balanced a posteriori error estimates for finite-volume type discretizations of convection-dominated elliptic problems. Computing 55, 305–323 (1995). https://doi.org/10.1007/BF02238485
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DOI: https://doi.org/10.1007/BF02238485