Piecewise linear finite element methods are not localized
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- by Alan Demlow PDF
- Math. Comp. 73 (2004), 1195-1201 Request permission
Abstract:
Recent results of Schatz show that standard Galerkin finite element methods employing piecewise polynomial elements of degree two and higher to approximate solutions to elliptic boundary value problems are localized in the sense that the global dependence of pointwise errors is of higher order than the overall order of the error. These results do not indicate that such localization occurs when piecewise linear elements are used. We show via simple one-dimensional examples that Schatz’s estimates are sharp in that localization indeed does not occur when piecewise linear elements are used.References
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Additional Information
- Alan Demlow
- Affiliation: Department of Mathematics, Malott Hall, Cornell University, Ithaca, New York 14853
- MR Author ID: 693541
- Email: ard11@cornell.edu
- Received by editor(s): July 22, 2002
- Received by editor(s) in revised form: December 15, 2002
- Published electronically: July 14, 2003
- Additional Notes: This material is based upon work supported under a National Science Foundation graduate fellowship and under NSF grant DMS-0071412.
- © Copyright 2003 American Mathematical Society
- Journal: Math. Comp. 73 (2004), 1195-1201
- MSC (2000): Primary 65N30, 65N15
- DOI: https://doi.org/10.1090/S0025-5718-03-01584-9
- MathSciNet review: 2047084