A posteriori error estimates with point sources in fractional sobolev spaces
| Autor: | Fernando D. Gaspoz, Andreas Veeser, Pedro Morin |
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| Rok vydání: | 2016 |
| Předmět: |
Numerical Analysis
Adaptive algorithm Discretization Applied Mathematics Estimator 010103 numerical & computational mathematics 01 natural sciences Finite element method 010101 applied mathematics Sobolev space Computational Mathematics Applied mathematics A priori and a posteriori Partial derivative 0101 mathematics Finite set Analysis Mathematics |
| Zdroj: | Numerical Methods for Partial Differential Equations. 33:1018-1042 |
| ISSN: | 0749-159X |
| DOI: | 10.1002/num.22065 |
| Popis: | We consider Poisson's equation with a finite number of weighted Dirac masses as a source term, together with its discretization by means of conforming finite elements. For the error in fractional Sobolev spaces, we propose residual-type a posteriori estimators with a specifically tailored oscillation and show that, on two-dimensional polygonal domains, they are reliable and locally efficient. In numerical tests, their use in an adaptive algorithm leads to optimal error decay rates. © 2016 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 33: 1018–1042, 2017 |
| Databáze: | OpenAIRE |
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