P. Houston, J.A. Mackenzie, E. Suli, and G. Warnecke. A posteriori error analysis for numerical approximation of Fridrichs system. Numer. Math., 82(3):433--470, 1999. Home/Search Document Details and Download
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A Posteriori Error Analysis for Stabilised Finite.. - Houston, Rannacher, Süli (1999) Self-citation (Houston) (Correct)
....boundary condition. Generalisations to systems and nonlinear equations are possible. Mesh adaptation in finite element discretisations should be based on rigorous a posteriori error estimates; for hyperbolic equations such estimates should reflect the inherent mechanisms of error propagation (see [6, 8]) These considerations are particularly im portant when local quantities such as point values, local averages or flax integrals of the analytical solution are to be computed with high accuracy. Selective error estimates of this kind can be obtained by the optimal control technique proposed in ....
....25, 2 , 5) where n,5 is the interpolant of 25 onto the mesh Tn used to calculate the approximation un to the primal problem (3.1) The mesh 7 a for the dual problem (3. 32) will be constructed via the fixed fraction strategy outlined in [13] using the local error indicator IIhdnallL2(n) as in [6], where na is defined to be the residual of the computed dual solution 25. In this example we first investigate the order of convergence of the error in the outflow normal flux as the mesh is uniformly refined. To simplify the presentation, we consider a model problem which ensures that the ....
[Article contains additional citation context not shown here]
P. HOUSTON, J. MACKENZIE, E. SfLI, AND G. WARNECKE, A posteriori error analysis for numerical approximations of Friedrichs systems. Numer. Math. (To appear).
A Posteriori Error Analysis for Stabilised Finite.. - Houston, Rannacher, Süli (1999) Self-citation (Houston) (Correct)
....and nonlinear equations are possible and will be remarked on where appropriate. Mesh adaptation in finite element discretisations should be based on rigorous a posterjori error estimates; for hyperbolic equations such estimates should reflect the inherent mechanisms of error propagation (see [6,8]) These considerations are particularly im portant when local quantities such as point values, local averages or flux integrals of the analytical solution are to be computed with high accuracy. Selective error estimates of this kind can be obtained by the optimal control technique proposed in ....
....e2,5(un, 5, n,5) where 2n,5 is the interpolant of 5 onto the mesh Tn used to calculate the approximation un to the primal problem (3.1) The mesh Tna for the dual problem (3. 35) will be constructed via the fixed fraction strategy outlined in [13] using the local error indicator IIhdnall2( as in [6], where na is defined to be the residual of the computed dual solution 5. In this example we first investigate the order of convergence of the error in the outflow normal flux as the mesh is uniformly refined. To simplify the presentation, we consider a model problem which ensures that the ....
[Article contains additional citation context not shown here]
P. HOUSTON, J. MACKENZIE, E. S/JILl, AND G. WARNECKE, A posteriori error analysis for numerical approximations of Friedrichs systems. Numer. Math. (To appear).
A Posteriori Error Indicators for Hyperbolic Problems - Houston, Süli (1997) (4 citations) Self-citation (Houston Suli) (Correct)
....of this approach greatly depends on the relationship between the size of the local error (u Gamma u h )j and the size of the local residual r h j . In this paper we show that the local residual on an element only controls a portion of the local error on , referred to as the cell error, cf. [3, 7]. Moreover, due to error pollution effects, the error on an element is influenced not only by the size of the residual on 3 , but also by the size of the residual calculated on the domain of dependence of the element . Thus, an h adaptive mesh refinement algorithm driven by residual based ....
.... section we shall address the following two questions: first, what portion of the local error is controlled by the size of the local residual Secondly, we consider the complementary question: what controls the size of the local error The material presented in this section is based on the papers [3] and [7] Here we shall restrict ourselves to an overview of the main results; the reader is referred to these papers for further details. Given 2 T h , we assume that the boundary is a non characteristic hypersurface for the operator L. On we consider the local boundary value problem L u h ....
[Article contains additional citation context not shown here]
P. Houston, J. Mackenzie, E. Suli, and G. Warnecke, A posteriori error analysis for numerical approximations of Friedrichs systems. Submitted for publication, 1998.
A Posteriori Error Estimates and Adaptive Methods for Convection .. - Ohlberger (Correct)
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P. Houston, J.A. Mackenzie, E. Suli, and G. Warnecke. A posteriori error analysis for numerical approximation of Fridrichs system. Numer. Math., 82(3):433--470, 1999.
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