Geodesic
Local error estimates and adaptive refinement for first-order system least squares (FOSLS)
Electronic transactions on numerical analysis, Tome 6 (1997), pp. 35-43.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: We establish an a-posteriori error estimate, with corresponding bounds, that is valid for any FOSLS L2-minimization problem. Such estimates follow almost immediately from the FOSLS formulation, but they are usually difficult to establish for other methodologies. We present some numerical examples to support our theoretical results. We also establish a local a-priori lower error bound that is useful for indicating when refinement is necessary and for determining the initial grid. Finally, we obtain a sharp theoretical error estimate under certain assumptions on the refinement region and show how this provides the basis for an effective refinement strategy. The local a-priori lower error bound and the sharp theoretical error estimate both appear to be unique to the least-squares approach.
Classification : 65N15, 65N30, 65N50
Keywords: adaptive mesh refinement, a-posteriori error estimates, first-order system least-squares 
@article{ETNA_1997__6__a17,
     author = {Berndt, Markus and Manteuffel, Thomas A. and McCormick, Stephen F.},
     title = {Local error estimates and adaptive refinement for first-order system least squares {(FOSLS)}},
     journal = {Electronic transactions on numerical analysis},
     pages = {35--43},
     publisher = {mathdoc},
     volume = {6},
     year = {1997},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ETNA_1997__6__a17/}
}
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AU  - Manteuffel, Thomas A.
AU  - McCormick, Stephen F.
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%A McCormick, Stephen F.
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%J Electronic transactions on numerical analysis
%D 1997
%P 35-43
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%I mathdoc
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Berndt, Markus; Manteuffel, Thomas A.; McCormick, Stephen F. Local error estimates and adaptive refinement for first-order system least squares (FOSLS). Electronic transactions on numerical analysis, Tome 6 (1997), pp. 35-43. http://geodesic.mathdoc.fr/item/ETNA_1997__6__a17/