J.A. Mackenzie, E.Suli and G.Warnecke, A Posteriori analysis for petrov-Galerkin Approximation of Friedrichs Systems. Technical Report NA 95/01, Oxford University Computing Laboratory, (1995). Home/Search Document Details and Download
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A posteriori error estimates in finite element.. - Achchab, Agouzal.. (1997) (Correct)
....attempt to answer these questions. The goal is to control the error in the computed solution and to optimize the computational process. The power of adaptivity in order to efficiently improve solution accuracy was recognized in the development of unstructred grid methods for Friedrichs systems in [11, 12]. These h adaptive methods are based on some a priori knowledge of the behavior of certain phenomena. While this approach provides some measure of the local error in the solution, the control of the error is not obtained in the same norm for the upper and lower bound. For the convection problem ....
....lower bound is in H Gamma1 norm of the residual. In [1] an other error estimator, in a norm jjj:jjj stronger than the L 2 norm, valid for all stabilisations (SUPG, GLS, GGLS, DW, using C 0 finite element method is given. For the Friedrichs systems, an analogous strategy is used in [12] to give residualbased two sided local a posteriori bounds for Petrov Galerkin approximation in weighted graph norm of the true error. In [2] the authors have presented a new a posteriori error estimator in the jjj:jjj norm for Friedrichs systems with boundary conditions described with a symmetric ....
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J.A. Mackenzie, E.Suli and G.Warnecke, A Posteriori analysis for petrov-Galerkin Approximation of Friedrichs Systems. Technical Report NA 95/01, Oxford University Computing Laboratory, (1995).
A Posteriori Error Estimates for Upwind Finite Volume.. - Kröner, Ohlberger (2000) (Correct)
....the grid. But these indicators give no information about the true error u u h . In this paper we shall exhibit a rigorous a posteriori error estimate of the form (1) in the L 1 norm in space and time. Earlier results related to this topic were published in [2] 3] 4] 5] 10] [14], 15] 17] 18] 20] for the nonlinear case and in [9] 13] 14] 16] 19] for linear systems of equations. In Section 2 we will fix the notation and present the main result. Furthermore we will quote the fundamental estimates from [1] and put them together in order to derive the main ....
.... u u h . In this paper we shall exhibit a rigorous a posteriori error estimate of the form (1) in the L 1 norm in space and time. Earlier results related to this topic were published in [2] 3] 4] 5] 10] 14] 15] 17] 18] 20] for the nonlinear case and in [9] 13] [14], 16] 19] for linear systems of equations. In Section 2 we will fix the notation and present the main result. Furthermore we will quote the fundamental estimates from [1] and put them together in order to derive the main result. Numerical examples will be given in Section 3. 2. Notation and ....
Mackenzie, J.A., Suli, E., Warnecke, G.: A posteriori analysis for Petrov-Galerkin approximations of Friedrichs systems. Oxford University Computing Laboratory, Numerical Analysis Group, Report Nr. 95/01.
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